Is it permissible to borrow with interest to pay off a large debt, or is it more preferable to sell the apartment we live in, knowing that selling it will psychologically affect the husband's ill mother, and that there is no other way to pay off the debt?

If there are no legitimate alternatives to repaying the debt, the creditor must grant you a respite until you find ease. If you are compelled to sell your apartment to repay the debt, and if it is possible to rent another apartment without undue hardship, then it is not permissible to borrow with usury. However, if selling the apartment would lead to severe and unbearable hardship, then it is permissible to borrow with usury to avert this harm, while limiting the amount to what is necessary to دفع the necessity, without any excess for investment. Necessity is determined by its extent.