Don''t worry, the courts will always prioritise the welfare of the children first and that includes their housing and as the main carer yours to.
If he is the mortgage holder he can''t stop the mortgage without risking reposession and ruining his credit history. He can''t force you to sell either, the only way he could do that is if he went to court to order the sale, but then the issue of providing housing for the children should be enough to put a stop to that.
If it is not a joint mortgage you need to register you interest in the house with the land registry.
whilst I agree in principle with Lostboy, it is not always that cut and dry.
He would need to be able to support the house repayment AND rehouse himself. If he cannot do both, you may need to sell.
In my case, I have three children, work part time and he earns a good wage. Although I did eventually get to stay in the house, I have to fund the mortgage payment and it only happened because we went to final hearing. The Judge asked if I had looked at social housing for myself and the children!