Thing is, if he is in financial difficulties, the judge will not award you the house on the basis that he continues to pay the mortgage. The judge will look at needs and resources. Clearly your needs will be greater than his because you have the 2 children. However, these needs (and his) have to be met out of available resources. If the resources are not there, then you will have to rethink. If there is sufficient equity in the house to enable you to rehouse yourself and the boys without recourse to a mortgage, then that might be the best option.
Also, his paying the mortgage is another tie, isn't it? I realise he will have to pay maintenance for the boys (and possibly also for you), but paying the mortgage is another matter altogether. The lender is unlikely to put the house in your name if someone else is paying the mortgage. After all, what would happen if he defaults (either because he hasn't got the money or because he feels like being a sh*t again)? You would be in far better control of your life if you weren't dependent upon him abiding by an agreement to pay for the house.
If he is in financial difficulties, how could he continue to pay the mortgage, maintenance as ordered and fund his own needs? And by needs, I'm talking basics here - a roof over his head and food, etc., not some fancy lifestyle he thinks is his due.
You don't have to move far away if you don't want to, but you may have to look at things realistically. The judge can't order him to pay for things that he cannot afford.
Just something to think about - as if you didn't have enough already.