Your right, they will tell you to forget about unsecured loans and concentrate on your mortgage.
If I was you, I would clear the cu loan as this is prob the only place you will be eligible for loans/credit in the future. Handy for emergencies etc. That's my thinking currently anyway personally.
Write to the bank,and register the letter. Tell them that a voluntary surrender would see you only repaying a portion of the outstanding balance and you would then be left with the remaining balance as an unsecured debt, and the cost of renting a suitable house in your area each month. This would lead you to the exact same, if not tougher financial difficulty you are experiencing now.
A split mortgage would benefit you as you all get to remain in the family home, they get an agreed repayment each month,and if things eventually change for the better, they will get a faster repayment.