My dog eats dirty diapers and pees on the floor

My 6 (ish) year old Lab/Staffordshire mix likes to break into the garbage and chew up my son’s dirty diapers. He does this when we’re out of the house. We try and remember to close all bedroom/bathroom doors that would contain any diapers in the garbage. But if we forget, he gets into it, chews the crap out of them (pun intended) and then it looks like he pees on the floor (not a lot, but like he’s marking his territory).
Does anyone know why he does this and how to get it to stop, other than making sure doors are closed?
We’re thinking about getting a second but I’m afraid he’ll pass on this weird/gross habit.
Thanks!