Finances after separation - advice needed!

[Usernamechanged]

I posted this in relationships but might be better here, so...

Quick background: two primary aged DCs. Trying to get my head around finances etc prior to inevitable separation. H the higher earner, not by loads. Would expect kids to stay primarily with me but see/stay with him couple of nights per week.

For kids’ stability I would like to try and stay in this house. I can just about afford the mortgage as is by myself. We have a good chunk of equity though and I can’t afford to stay if he gets half, I.e if I need to pay him off.

The amount of equity is broadly equivalent to the child maintenance he’ll pay till kids are 18. Is it ridiculous or even legal to agree that I keep the house and equity but he doesn’t ever pay maintenance? I can survive financially without it and would rather keep the house.

Would welcome advice.

And as follow-up:

I don’t know if he will agree but he might. He’s almost 20 years older than me and has a very big pension which he can access on the next couple of years if he wants. I suspect if I agreed not to make a claim on that he might go with it.

I don’t want to shaft him but I do want to ensure stability for my DCs, and not moving at the same time as parents separating is part of that. (My parents divorced when I was a similar age and we had to move and it just added to the trauma - hence I’m a bit hung up on this.)

I think you sound fairly reasonable in putting this forward - he would then need to weigh up the "value" to him of not paying monthly maintenance and keeping his full pension. Is he able to buy his own property though? This might be the sticking point if he then has to rent because a lump sum of equity is tied up in your house?