If as you say the mortgage on the property is in the names of your SIL and her ex-husband, she will have two groups’ people to convince. (1) Her ex-husband that he is prepared for his name to be removed from the mortgage document, he may be giving any equity in the property to his ex-wife. (2) The mortgage company who are interested only in having the mortgage paid, they will not care by whom, at present they have two names each jointly and severally liable to repay the mortgage in full, which she will be asking to reduce to one. She must first be able to deal with the payments and preferably have paid it for several months; if she has and has agreement from her ex-husband she should be able to convince the mortgage provider to have the mortgage document in her sole name, without a guarantor.