Sounds like his jealousy of the new dog and fear of being abandoned again is causing him to make sure everyone knows this is his territory, so he's marking it...
If it was a human I would say it is a weak bladder or kidney infection...or your dog is severely scared of something or someone in the house...my nephews dog is scared to death of anything black. Probably a case of abuse before he got the dogs from the pound...but since I can not read the dogs mind you would have to take the dog to a vet and see if anything physical is wrong with the dog..
It could be him marking territory, take to vet, have kidneys and bladder checked. If all is well then I am stumped!!