Finance after divorce

My ex wife and I have recently divorced after she cheated but we hadn't settled any of the financial side. We are just about to start mediation. I currently pay all the household bills and mortgage and we are still living at the same property with our 3 children.Basically what she is proposing is that she stays in the home with the children and I move out and rent. The mortgage is in both our names and is currently £1600 pcm. She wants to pay £1000 and I pay £600 on the condition that she will not go to csa and the house cannot be sold until our youngest is 18. If I agree to this private agreement what stops her going to csa anyway and when our youngest turns 18 can I force the sale of the house or I will never see any money back from the house. I wanted us to sell the house which has about 150k equity and use this to set both of us up with new mortgages or private rents but she says 60% of the equity is not enough for her to rent because her wage is lower than mine. Any help will be appreciated

Nothing can stop her applying to CMS if she chooses to.