Try “I Statements”. It’s natural to say what you said above, but it comes off accusatory and non-trusting.
From one lawyer to another your definition of “the conversation was going nowhere” is “she did not begin to agree with me.”
The conversation went everywhere it needed to go. You framed the discussion as one in which your wife failed to appreciate an objective fact. However, the danger was not an objective fact here, or even a near-certainty. It was a series of fairly tenuous potential risks you were not comfortable with.
Instead of putting on your Persuading Hat to convince her she is wrong and you are right, maybe next time state what the actual problem is, which is that, rightly or wrongly, the situation made you feel nervous.
"I am feeling uncomfortable with this - It is making me feel anxious thinking that dog might dart into the road. I know you don’t think that would happen and I guess it probably won’t, but it would make me feel a lot more comfortable if we staked the dog while you’re working in the garden. "
I have a feeling as a woman and a lawyer, that she would be a lot more receptive to your idea of staking the dog if you admit it is to make you feel better and not because You Are Just More Right Than Her About Reality.
Well put.
We decide based on who wants it more/cares more. But this is important: who wants it more/care more is NOT the same as who is willing to fight longer or be bitchier about it. I’m probably more willing to be bitchy than my husband, so if we used that metric, I would have always gotten my way for about five years and then he would have left me. Luckily, I temper that temperament (can be doesn’t mean have to be) and instead we have a Long Boring Conversation to determine who has more of an interest in the outcome. The conversation works because we both have a sincere interest in determining the truth, not because we are haggling to get our way. Again, if it were haggling I’d win because I am more stubborn. But I would have lost the marriage by now.
In your case, I think that your distress over the risk of the dog dying was way more powerful than your wife’s pleasure at having the dog around, so you should have gotten your way.
I’ve actually heard of couples who use a numerical system to decide things: You might have said to your wife “this is about a 7 to me. I am really uncomfortable knowing the dog is out here” and your wife could have said back “It’s more like a 3 to me. I like seeing him play and think your concern is baseless, but if you care that much, take him in”. This sort of thing can work very well if you are both honest about how you feel, not looking to exaggerate in order to “win”.
Hello Again is absolutely correct here. “I feel…” statements are like magic when communicating. The way you brought it up to her would make anyone feel blamed and condescended upon.
I’ve always been told that sighthounds are NEVER really safe off-leash.
I have to keep in mind the circumstances. Trust me when I say my wife loves control. Due to our daughter’s medical circumstances, my wife has lost control of so much … huge things in life that are of great value. So when I come in and strip her of one of the few things she can control or thinks she should be able to control, that can’t sit well with her.
There’s a lot of good advice here.
Basically a counselor is going to tell you two things:
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You and your wife have to work out a way to communicate that you disagree without the other person feeling like they’re being personally attacked.
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You and your wife are going to have to work out some things in your stuff management styles, where she accepts that you’re a little high-strung about how things are, but don’t want to raise a fuss about it, and she’s more laid-back about how things are, but is perfectly willing to defend her laid-back choices.
Of the two, I can’t really say which is more important here.
If you want to try some things first, one biggie from note 1 above is to try using self-deprecatory statements whenever you’re more worried about something than your wife is.
So, for example, the conversation you recited would go more like this:
Me: That looks risky, shouldn’t he be on a leash?
Her: No, he’s fine. We’re watching him.
Me: I know, but you know how paranoid I am about these things. I know it’s not very likely, but it just makes me nervous. (this is three times you’re putting yourself down in one statement: 1-paranoid, 2-“not very likely” undermines your decision-making skills, 3-nervous)
Her: No, he’s fine the way he is.
Me: (Now seeing that each of them had their primary focus on doing other things … namely, watering plants and playing with baby) You know me, now that I’ve seen him, I won’t be able to concentrate for worrying about him! I know I get too worked up about these things, but I’m going to get the tether for him anyway - just to set my mind at ease. (Again with the self-putting-down, and also telling her outright what you’re doing, instead of heading inside as if she won, and then coming back with the tether).
Basically the goal is to make it seem like you’re the weird one who cares too much, not that she’s the slack bad doggie parent who doesn’t care about her dog getting hit. If you’re a little over the top with it, it also lets her roll her eyes at her friend about the freaky weird husband she has to deal with, which lets her feel superior to you, even though you just got the outcome you wanted (dog on leash, no fight with wife.)
This approach works pretty well for any type of disagreement in public. A little less well in private, but it still helps.
All it takes is a willingness to gratuitously insult yourself when you’re making requests that are out of her comfort zone. 
(Despite the flippant tone, this is a serious suggestion - I taught my husband how to do it, and he gets on much better with his four sisters now.)
Even if you didn’t have an answer in mind when you asked her, the question was pointless.
You did not ask her a factual question. She wasn’t going to come into the discussion with the latest statistics on cases of negligent supervision of dogs.
The question was very subjective. You basically asked her if she could watch the dog. The answer was going to be either she could or she couldn’t. I would avoid asking those questions in the future if you’re not going to be prepared to accept one of the possible answers.
Once she said that the dog was fine because she was watching him, any further questions from you probably made it look like you didn’t think she wasn’t capable of watching the dog.
This conflict had two dimensions. One was keeping the dog safe. The other was not embarrassing your wife. You ignored the second dimension. Next time just be aware of what could embarrass your spouse and try to avoid it.
ETA: You could do things as I suggested, but Hello Again’s suggestion is ten times better.
Well, I guess you could take my approach to people insisting it’s fine for them to feed my dogs half a pound of bacon apiece. Fine, but if they get pancreatitis, you’ll be the one cleaning up puke and bloody shit and paying the vet to hospitalize them for a week, which will probably run about $1200 per dog. So far nobody’s taken me up on that; somehow what’s a totally acceptable risk when I’ll be the one paying the piper isn’t so acceptable when the consequences are all theirs.
Your conversation sounds like an echo of my FORMER marriage…and a great deal of why it’s former.
You asked her what she thought. She told you. You then argued - and from her point of view, you were arguing with what she thought. You were telling her that not only her actions, but her very thoughts were wrong, only you didn’t have the balls to actually say it. It’s passive-aggressive and infuriating to a control freak (like me). You weren’t really asking her what she thought, but neither did you tell her what you wanted her to do up front.
Next time, tell her what you want. Tell her what you need. Don’t expect her to decode your questions and do all her thinking as if she was you.
“Honey, the dog being off leash makes me nervous because she ran from me last week when I was watching her. Would you like me to bring out the tie, or should I bring her inside?”
True, she can still argue with you, but at least then there would be greater justification for being annoyed with her.
I’m listening to you all. Thanks for the input.
So let’s say the conversation went differently. Keep in mind the context that I’m on my way out to get us lunch, so I really don’t want to leave the house with the dog off leash. I would be a wreck as I drove away.
Me: Hey, the dog being off leash really makes me nervous, I’d like to put him on a leash.
Her: He’s fine. We’re watching him.
Me: I know, but I don’t think it’s safe and it makes me very uncomfortable.
Her: He’s fine. Don’t worry about it. Can you get us some lunch?
Me: 
________________________.
(If your answer is different than those already posted).
When first learning to change your style of communication there is an additional hurdle that sometimes gets overlooked. You have to be willing to sound a little scripted, to use words and phrases that don’t necessary come naturally.
For example “I statements” (which is excelent advice) or the self-depricating statments as suggested above may not roll off your tongue the first day or even the first month. Give yourself permission to sound a little stiff and feel kinda like an idiot at first while you adapt and become fluent in the new communication style. The more you use the words and phrases the more natural they’ll feel.
ETA in response to your post above mine.
Be honest about your feelings. “Honey, I really am worried I’m gonna fret about this all afternoon and just not let it go. Are you willing to indulge me on this even though you don’t agree with me? I’d appreciate it.”
Theoretically, she wouldn’t get embarrassed if you took action yourself. You could get the leash and say “I just don’t trust the dog to stay put.” This way it’s about you being nervous, and not about her being wrong.
“You know me, now that I’ve seen him, I won’t be able to concentrate for worrying about him! I know I get too worked up about these things, but I’m going to get the tether for him anyway - just to set my mind at ease.”
"I am feeling uncomfortable with this - It is making me feel anxious thinking that dog might dart into the road. I know you don’t think that would happen and I guess it probably won’t, but it would make me feel a lot more comfortable if we staked the dog while you’re working in the garden. "
I get the feeling this may result in another round of something like “Oh, don’t worry, he’s fine.” I would hope that she would respect my discomfort.
You don’t say what kind of attorney you are, but surely you must have experience in a contract negotiation or a tort or a criminal case where the party of the first part and the party of the second part don’t agree, and you and your counterpart on the other side have to negotiate some sort of mutually agreeable settlement. What do you do then?
More to the point, why can’t you and your wife use those kind of negotiating techniques to resolve the situation rather than “trumping” each other?
All I can say for myself is that when my wife and I are facing a real crisis (as wehn our daughter had health problems) it makes the petty stuff seem really. . . petty.
My action unilaterally trumps her control, and that really sets things off.
Civil litigation .. but a lot of that is telling the other party they are wrong, arguing why they are wrong, arguing people into a box, and then agreeing to disagree and bend anyway because the cost of failing to bend is higher than the cost of not bending. So that adversarial style doesn’t work here.
Unfortunately, each of the little arguments is about petty things in the grand scheme of things, but the bigger issue here is not the petty substance of each argument. Rather, it’s about how petty differences on routine matters end up as big deals due to ineffective relationship communication.
If she really doesn’t respect your feelings then your problems are much bigger than what anyone can solve from the few facts we have in this thread.
Well, if she has control issues, then that’s another problem. It’s certainly possible, but I don’t see any control issues in your OP.
We had a conversation and you all were exactly right. I came at it with an accusatory question, followed up with a debate, and ended with unilaterally tossing aside her judgment and replacing it with my own.
The conversation would have been much different if I had said something to the effect that I appreciate her wanting the dog to be outside, but it made me overly nervous to leave the dog unleashed even though she was watching him diligently.
I gotta work on those “I statements.”