Until the divorce is final I would not purchase anything major like a home, he may claim half the increase in equity or something else, who knows, it is best to just wait.
If you are concerned about him being in your home have your attorney file a motion to have him removed and you move back in. If you have the kids nad can pay the mortgage, then they most likely will give you the order. If he has the kids then they probably will rule for him to stay put.
I laughed when I read your comment about him burning the house down before he would let you have anything. One time on this site there was a women who her and her husband owned a dog kennel business and a home on the same property. She filed for divorce. The day he was served papers he came home from work, spread gasoline on everything in the home and the kennel and all of the vehicles that they owned and set everything on fire. It burned to the ground, home, business and all. He was arrested and there was nothing left to split in the settlement of the divorce. The insurance didn't cover the burnt property as the owner (half owner, she was the other half) had done the damage so no insurance just the debt of the mortgage, the car loans and the business loans. She got all the debt and he is serving many years in prison for his acts.
Hopefully yours is not this bad. Mine was very bad, almost as bad as hers, but when I hold my own pitty party I remember her story and it helps me think that maybe I can make it another day.

I don't know if all states are the same on this, but in SD when the divorce papers are served a restraining order is put in place that prohibits either party from making a large purchase without written consent from the other party.