Take him back to the vet. And take him out a second time at night, he's your baby, so if you have to get up in the middle of the night to feed or change your baby, the same applies here.

I'm sure you'll figure something out, he's probably miserable having to go pee inside too.
Do you have a crate for him? If not perhaps you can try that, after he gets used to it, a dog won't want to eliminate that close to themselves unless there is something seriously wrong, perhaps kenneling at night will help.