This is 100% behavioral. 1st thing, is he has a place to hide in the laundry room, that is not good. He needs to realize that he is "always on" and there is never a place to hide. You could keep him leashed with a rope or string to help break this behavior. He will learn that there no running away and is always "on leash" as his behavior improves you simple cut the rope shorter and shorter till he doesn't need it but always thinks he's attached. Kenneling is good, but it must never be a punishment, this will only make him hate the kennel and not want to go in or whine when he is inside. You need to reinforce the positive peeing as well as punish the marking. Not just punishment but praise too. When he pee's outside let him know your happy with him. Attention and jealousy may also play into his behavior. Is he jealous of the attention other family member is get over him?

This habit can be broken with neutering, it may help but I'm with your vet on this one. The more attention and training he receives the more he will try to please you and he'll know that peeing makes you mad. Also you need (and I mean need), to get whole whole family on board with training and have everyone follow the same regime.
Good luck, and remember there are no bad dogs!