You can do this! Of course, I am not a lawyer and don't know what state you live in, but in mine, if it gets to court, they take into account who "gets" to work because the kids are in childcare - which in this case would be both of you - so I think its reasonable to expect he would need to contribute more for that.
Find that lawyer and talk about options - including how much you are dreading selling that house. Maybe they have some suggestions that would allow you to move before it is sold so that you don't have to deal with all the stress of keeping it walk through ready.
When you interview lawyers, make sure you stress how important prompt feedback is for you, since that sounds like something that adds to your stress level.
