Right...most of what I would have said has been said by other people. I'll tell you what I think about it though...
Don't make any irreversibly decisions when you go to mediation. If you need to go to court to straighten this all out, then go. At least then he can't agree to things and then change his mind later.
Consult a solicitor or a citizens advisor and find out what the law says about your situation. I think you will find that what others have said here is true, you should be entitled to keep the roof over your children's heads and he will have to pay to keep it there. My cousin had a deal whereby he had to pay a proportion of the mortgage but when it was all paid off she owned the house.
Find out what tax credits and benefits you can claim to help you.
Shop around for a better mortgage deal. Sometimes it's worth paying the penalty to escape if the alternative deal is good enough. Otherwise contact your mortgage provider and ask if you can extend the term and lower the payments.
What kind of a mortgage do you have? If it's a repayment mortgage you can switch to an interest-only mortgage which will be much cheaper. You will still benefit from the house increasing in value over the years and in the future you will be better placed to start paying into endowments to cover your mortgage.
I would most certainly rent out any spare rooms, as a means of raising extra funds it can't be beaten. But do check that it won't spoil your chances of claiming benefits or tax credits and weigh up which is more valuable to you. If you do rent a room make it as nice as possible so you can charge more rent and attract somebody nice to live there. Get references and lay down ground rules.
Always bear in mind that one day your children will be at school full time and you will have to opportunity to earn more. You just have to keep the boat afloat till then.
If you want to take on extra work there is always party plan selling like Ann Summers or clothes, books, whatever, with this kind of job you can work as and when it suits you. I did Tupperware for years and years and the money was quite good. I was always there for the school run.
Your ex's remark about not caring where you live was revolting. Adults fall out but what about his children? I wouldn't have any compunction in getting every penny you can out of a creep like him.
Essbee, do email me anytime if you want to chat. It's quicker than hoping I'll be on mumsnet when the thread is still active! Although I must admit I'm on a lot - don't know how I missed this!