Yellow rocket fountain.

I know your pain. My rescue of three weeks does that

Cute but sad, sorry

If I was a dog, I, too, would pee in happiness to find out the human being taking care of me didn't die while out, thereby leaving me alone

My dog pees when she's excited too. Everywhere. It's cute, but not on guests shoes!

I don't know your dog's personality, but the best way to stop the peeing is to build up your pup's confidence. Peeing can be excitement or nerves, but the exposed belly is submission. A submissive dog is not a bad thing at all (they're often easier to work with than dominant dogs), but a dog THAT submissive is probably worrying unnecessarily and would benefit from a boost in confidence. I wish I had some advice for you, but I have very little hands on experience with dogs as submissive as yours. I don't know if I've gotten lucky or if it's the way I raise and train them, but I have ended up with very confident dogs my whole adult life (when they were MY dogs, not family dogs). So my advice to you would be to find a trainer who has experience with submissive dogs and ask about ways to help boost that confidence. In the meantime, you could make use of belly bands to protect your floors, clothes, and anything else he pees on when he gets that way. From what I understand, fear/excitement peeing can be awful to deal with and many dogs get dumped in shelters when the owners stop tolerating it so I commend you for sticking with your dog despite his flaws.

My puppy does this when I get home too

Let me guess, Dachshund?

i laughed way too hard at this

It's usually a sign of submission when a dog shows its belly in greeting but when it urinates, too, it's a good bet that the animal has been physically abused in some way in its past. The best way to discourage this behavior is to ignore your dog for a few minutes until it calms down and is ready to greet you properly. Also, show him/her lots of love and affection. Abused dogs can sometimes make the best pets.