I’ve recently had to move in with my parents due to a lack of employment and it’s been a relatively smooth transition save for one thing. Both households had a dog. Mine is an elderly shepherd mix, medium sized dog. Theirs is a 2 year old toy poodle. The dogs have known each other since the poodle was a pup and while they never played together (mine doesn’t play), they pretty much just ignored each other. Well ever since we moved in, the poodle has become a yipping, yapping nightmare. EVERY time she sees or hears my dog, even if it’s across the house (wood floors, so clicking nails), she starts barking like crazy. If my dog walks by her, it’s like a switch is turned on and she just runs after her yipping her head off. True to her nature, my dog has been completely ignoring this little terror, not even acknowledging her presence really. At first we assumed it was just the poodle being unhappy with the new dog in her territory but it’s been over two months and if anything, she’s getting worse. It’s driving everyone crazy to be honest and we can’t figure out how to make her stop. Probably related to all of this, she barks the same way whenever we come home. She knows it’s us, she sees us and STILL barks that annoying high pitched bark. Obviously yelling at her doesn’t work, as my mother has found out since it’s her preferred method of dealing with it. I’ve considered getting a spray bottle and spritzing her in the face with water whenever she barks but I’m not even sure this will work. I’d like to figure out why she’s doing this and deal with it but I’m not even sure what it could be. Hoping that someone can offer some advice 
May I direct you to this thread of mine?
LOL, that’s not likely to go over well with the parents.
Dealing with very ingrained and hard-coded behaviors such as barking at “intruders” may be very difficult to eradicate. Be forewarned.
I know I will probably be called the worst dog owner ever for this suggestion, but here goes:
How I taught my dog not to do something:
Whenever it did something I did not want, I immediately yelled “NO!” directly at him and shoved/smacked him (NOTE: This “smack” is not painful in the least, trust me. The “smack” is an attention getting jolt. Spritzing with water will probably work as well). The result of this interaction is that the dog is not doing what it was just doing a second ago and you have its full attention. This needs to happen within seconds of the violation so they have a clear connection of action-reaction. This means you may have to follow the dog around for a while, because he needs to know that you disapprove each and every time.
This notifies the dog pretty quickly that this behavior is not tolerated. You have to be consistent, and never wavering.
You can’t follow him around for forever, but luckily you can hear him barking even when you aren’t in the same room. If you hear him barking at your dog, you should go running to find him. By the time you get there, you probably won’t have to even touch him because he already knows you are ticked and are coming after him.
This has worked well for my dog, and he doesn’t touch ANYTHING on the floor that has not been given to him. He does have a fairly high desire to please his master, and that helps tremendously.
If you have a dog that thinks it is alpha or that you are not over it, that is a whole different problem.
Okay, on a more serious note - does the yappy dog do this EVERY time? If not, try rewarding positive behaviour. Keep treats handy and every time he doesn’t bark give him a treat and praise effusively. Also try bringing them together specifically to give treats and attention. Stop when the yapping starts.
It’s going to take a while, good luck.
Google on barking shock collar.
Our dog trainer has recommended keeping a spray bottle with water handy and spritzing the beast when it commits errors of etiquette like barking (not too effective on our Labrador, who after all is a water dog).
What did work very well was when the dog barked in its crate - we were directed to go up and shake the crate vigorously (“Crate Earthquake!!!”). Dogs do not like Crate Earthquake. Perhaps you could adapt this technique to household barking (pick up and shake the dog? stomp on the floor?).
I’m betting the poodle isn’t getting enough exercise. A tired dog is a well-behaved dog, and two years old is still in the high-energy just-past-puppyhood phase.
I once taught a barky dog (a collie-retriever mix, too big for yappy) to be less vocal by teaching her to bark.
In other words, I gave a name to the barking, then told her to stop, and rewarded her when she did stop. Over time, she’d go “BARK BARK BARK…OK, I’m quiet now, where’s my treat?” But it took a long time, and she only barked at specific things, not everything non-stop. Over time, 30 minutes of uninterrupted barking at a noise outside and night would turn into a few woofs, I’d tell her “thank you, good girl” and she figured her job was done. The important thing, as Moonlitherial said, is to reward the behaviour you want.
IMO, in some dogs barking is often hardwired and a really difficult behaviour to fade. Barking (or “voice”) is a desired and bred-for trait in some breeds, mostly hunting and some herding dogs.
You could try bark-stop type collars, some squirt water or lemon juice or something bitter, others deliver a shock. The better ones can be set so the dog is allowed to bark for several seconds (after all, it’s a dog thing) before going off. I’ve never used one and think they’re sort of unfair if no serious effort has been made to socialize and train the dog before springing this sort of thing on it, to be honest, but they apparently work on some dogs (although certainly not on all.)
I am guessing the poodle (unlike your dog) is not well-trained generally. Does the poodle get to leave the house, go different places, get exposed to a lot of different people, dogs, environments? I am guessing not - and the barking is some sort of mixture of uncertainty, frustration, excitement. Dogs that are highly socialised are pretty blase about things generally, are more confident, take things in stride, and don’t get too excited or stressed about changes in their environment. Maybe obedience classes, a good structured environment helps a lot of dogs with reactivity issues.
There’s always debarking, but that tends to set people off in howls of outrage. I’ve had multiple dogs my entire life and personally have no patience for noisy dogs, so I avoid those breeds. If I had a dog that was otherwise awesome, I’d have it debarked if all else failed. It’s less invasive than spaying or neutering and better than constant nagging, squirting, shocking, or getting rid of the dog. I’ve known several debarked dogs - they can still bark happily all they want, they’re just not irritating the crap out of everyone.
Exercise and training are really important, I’d try everything possible before going to a surgical option. But I did want to throw the option out there - this poodle could live another 18 years; does anyone want 18 years of reactive yapping?