If you want to do the moral thing, you sit down with your husband, you explain ALL of his rights, what he is entitled to under the law, then you negotiate with him. You could try something like this:
"The law says you are entitled to half the equity in this house. It also says you will be responsible for child support payments. The judge will not let you get out of that. You could agree with me in private not to pay it and for me not to seek it, but be aware that if I lost everything tomorrow and decided to come after you for help, a judge could mandate it. So you have to decide whether you trust me to keep this agreement.
Also, I don’t really want to sell the house, or borrow money to pay you out. And in the end, I think you’ll wind up paying as much for child care as your half the equity is worth. So here’s what I’d like to propose, and we’ll have to get a lawyer to look at it and make sure it’s kosher…"
And then come up with some creative ways to protect you and to protect him, and to make sure everything is divvied up equally. For example, you might be able to draw up a payment schedule to him to pay out his share of the equity, that just happens to match the amount of child support he has to pay. The numbers cancel out, and your debt to him slowly diminishes. If your daughter gets to the age of majority and you still owe him money, you agree to pay a lump sum. If the money runs out before she’s of age, he starts paying you alimony.
Or, you could give him the cash, but plead with the judge to have it tied up in a trust for your daughter because he’s too irresponsible to make payments.
Ultimately, if he says, “Give me my half the equity, in cash, and I’ll pay the child support when ordered to”, you should agree to that too.
There are very few divorces where everything balances out perfectly. Usually one partner winds up contributing more than the other. This does not matter. It’s not just that the law states that you share your assets after you got married, it’s that you knew this, and married him anyway. That means you have a contractual obligation. By screwing him out of what you agreed would be his when you married him, you a breaking your word.
There is no way I can spin the choice to attempt to play on his ignorance and laziness by screwing him out of what’s legally his as anything but unethical.
Usually it’s men who make this argument. They have the high-paying jobs, and the wife stays home. Then they get divorced, and the man in incensed that he has to give her half of what he earned. We generally don’t look kindly on men who try to weasel out of that arrangement, and neither does the law. It should be no different when the tables are turned.
You could also look at this another way - maybe your husband was lazy and shiftless because he could be. You were the breadwinner, he didn’t need to work. You were apparently cool with this. It was the arrangement you both had. Had you never married, he may have been forced through circumstance to improve himself and build his own career. This is one of the arguments that has been used to ensure that housewives who have never worked still get half of whatever the family earned - had she not been married, she would have had her own income. If the marriage was set up so that she didn’t work, that doesn’t mean she can be tossed penniless onto the street at some arbitrary time in the future. Hence the general rule that marriage is a partnership and any assets accumulated during the marriage are split.
BTW, are you also checking to see if he gets half of your 401(k) or any other retirement benefits you may have accrued while you were married? I suspect he may be able to make a claim there as well. There are plenty of cases where one spouse might forego a retirement savings because the other spouse’s retirement plan is enough to cover both of them. So the one spouse saves the money and they use it for expenses, travel, whatever. Then a divorce happens, and suddenly one spouse is left without any retirement funds.
He should absolutely get his own lawyer. You should tell him to do so. You should insist on it. You should both make sure that the law is fully complied with and that any settlement you make is made with each party in full understanding of their rights and obligations. Anything less is taking advantage of the man.
