I hope all works out for your and the little guy. You need to look into housebreaking him. You just can't let an untrained dog have free run of your home and someone has to take responsibility for taking him out.....frequently. Maybe give him an enclosure he can stay in like a puppy play pen or some other area to stay in when no one is there to watch him.
There is still the possibility that he may have actually belonged to someone and just got out and got lost. If he is a Yorkie then it is very possible that he made a break for it. They love to run and don't realize the dangers of getting too far from home. Maybe consider putting an ad in the paper but be careful not to identify what he looks like or what kind of dog he is. Make any responder give you identification of the dog they lost.
A long haired dog can get really messy looking really fast when out on it's own. If no one is missing a little darling like him then you are very blessed to have him and he is privileged to find a new home and family that loves him. If there is any chance you wife will change her mind it would be best to find him a new home now. It is very difficult on these dogs to have to be re-homed over and over but hopefully you now have a new much loved furry family member.
