your fiancee and you will be on the mortgage for the first home even if you move out. Can't say if the mortgage will release you without a refi. this means you're on the hook if they fail to pay. Being obligated, might affect the ability to get a mortgage of the second home or result in a higher interest rate. this is just a warning but it has happened. you also own the first home. if something happens, there will be no step-up in basis so you can avoid gain on sale. perhaps , it would be advisable to consult a lawyer for estate planning regarding your elderly parents.
