What tricks could she pull on you?
Your name would be on the mortgage. If you stop paying up, you would have to go bankrupt and the house would go from under the lot of you.
She could kick you out, separating you from your kids. You would be pretty much obliged to keep paying the mortgage in order to not go bankrupt, and to keep a roof over your kids heads. If you stopped paying out, in the divorce her Lawyer would present this as what git you are. If you carry on paying out, you can guarantee that she'll get the lions share of it.
In a situation like this, she holds a lot of power. All she has to do is hint that you're violent towards her or the kids, or even that she's afraid you might be, and you're in big trouble. Or she could move another bloke in, and get friendly with him. That wouldn't be a situation you're likely to be able to stick out.
Ultimately, for a lot of people, money can be the be all and end all. I know of siblings who have become bitter enemies following disagreements about money. If she's willing to screw you over once, she'll be willing to do it again, and this time she could really screw your life up. If she were so minded, you could end up bankrupt and with naff all access to the kids.