Ninja obviously it's your personal circumstances and they are unique to you but I'm not sure why H thinks you have to buy him out immediately.
The priority is a roof over the kids' heads. H is entitled to his share of the equity of the house of course but not if that means making the kids homeless (eg if you were to default on a bigger mortgage cos you couldn't afford it).
Even if you wanted to, would the school give you extra hours anyway, at this time of recession.
My best friend had a similar circumstance in that she and the kids stayed in the house. She could just about afford the mortgage but had no capital to pay off exP, so he paid reduced maintenance on the understanding that when the house was sold, he would get a share calculated on the value at time of sale, not at the time he stopped paying the mortgage IYSWIM. ie his share appreciated over time cos he didn't get his share when he moved out.
It was all agreed with a solicitor and in writing.
I don't know your circumstances but if the kids will mainly live with you, get some legal advice (I'm sure you are) about what you actually have and don't have to do.
It's a horrible thing to say/think but if this really is it and the marriage is over, then you have to become quite selfish to make sure you get a fair deal. If handled right, his relationship with the kids is another matter (ie it shouldn't get tainted by you looking after your future).
This may be teaching grandma to suck eggs and do what is best for you but I wanted to say it as I can remember how f**d up my head was when I left exH, and that was without children!
(Carrie get DH up to bed dear! :) )