What usually happens when couple's divorce and there is a joint mortgage, is that one of them will take over the mortgage. In your mother's case this didn't happen and more than likely because the lender didn't feel she could take over the repayments on her own - although she has obviously proved them wrong. In these circumstances a couple can come to an agreement on the split of the proceeds, rather than 50/50 - 80/20 for example.(posted 7957 days ago)Are you absolutely sure that your father will be entitled to half? If you haven't spoken to your mother about the divorce settlement, have a word with her - to ease your own mind as well as being able to understand exactly what is going on. If need be, then get copies of the paperwork from the solicitor who dealt with the divorce.
If it turns out that your father might be entitled to half the proceeds, then your mother can actually fight this to get a bigger share for herself, as she's been solely responsible for the mortgage, she can prove how much extra she's paid into the home. This might mean having to go to court however, but if there is a fair amount of money involved it'll be worth it. As this would be related to the divorce, it would be best to go back to the solicitor who dealt with the divorce - if she's eligible, your mother could get Legal Assistance for the costs.
Has your mother had a word with other lenders to see if they are willing to help? Just because one says no, doesn't mean the others will. Depending on how much the debts are it may be possible to negotiate lower payments to creditors, or perhaps consolidate the debts.
If your mother does decide to sell the house, then I'd suggest that she gets some legal advice first, and find out exactly how much, if anything your father would be entitled to from the proceeds and then get the same firm to do the conveyancing, so there are no mess-ups.
Sorry I can't offer much more advice than this.