You say that he is good when you are home but not when you are away. First thought is he is anxious when you are gone and the stress causes him to soil. But if he were truly trained to use the pads he still should. Second thought is that he minds his manners when you are home but when you are gone he claims the space to make it his own. The small amounts of pee can be indicative of a UTI but then it would happen regardless of you being home or not. So the small amount of pee means that he is choosing to sprinkle his scent everywhere which is marking behavior.
Little dogs can be tougher to house train because their mistakes often go unnoticed until it's too late.
Basic rule is - if your dog is acting like a puppy then he gets treated like a puppy until he proves that he can be trusted. So if you are not able to watch him closely so that you can actively teach him good manners then he needs to be managed in a crate or small room and be taught to hold his needs until he is let out. If you are using pads exclusively (not taking him out to soil) then if you use a small room to contain him you could put a pad in there. Sometimes we have to accept that managing a problem is the first step to retraining.
You can't afford to make your roomies anymore frustrated and rehoming should not be part of the plan. It is not okay to pass off an untrained dog to someone else because he is likely to just be repeatedly rehomed and that is not fair to him.
Love Them & Lead Them,
~Elizabeth & Doug
Dog Training the Way Nature Intended