Should I leave the girl who stipulates a separate apartment from the mother, fearing that I would be neglecting the right of the mother whose father passed away and who would be alone?

The Lord's pleasure is in the parent's pleasure. Therefore, look for a wife who agrees to live with your mother and take care of her, seeking reward for serving her. For if this is not legally binding on your wife, it is binding on you if your mother is in need of service and care. And Allah does not waste the reward of those who do good.