All depends on your state's laws, and on what you two decide on, and on the judge's whim.
Nothing is automatic. Often I think the custodial spouse has a good shot at keeping the house too but it's not law.
Here in WA, we are a community property state. Not all states are. Here, if you had bought the house before marriage, then it is yours. It is not split in a divorce. If you bought it during marriage with joint funds, then it is community property and is subject to division in a divorce. It can be awarded to either spouse, or ordered sold and proceeds split. It's not an automatic 50-50 split in this state though, the law calls for 'equitable' rather than 'equal' division of property. That means that if you had paid the most towards the house, and had custody of the kids, then you could argue to keep it and not split it, or pay her only what she'd put in towards it. Here in WA, if you bought the house during marriage but paid for it entirely with separate funds (inheritance, or money saved from before marriage), then the house would be yours. On the other hand, if SHE bought it, then you're probably SOL even with custody of the kids.
You can see how complex it is, and it varies by state, and by situation, and by judge's whim.
Don't do this alone if there are children and real estate to divide. You should have a good lawyer. And don't expect to get your revenge on her through the division of the kids and house. If you go in to court angry and venting, you'll come off looking like the villain to the judge. However awful you might think her behavior has been, you chose to marry her and have kids with her and buy a house with her. We're none of us totally innocent victims in these relationships. All the judge is going to see is what you present in court so make it reasonable and rational.