Dog constantly has poop on this butt

Dog we are discussing is my grandmas 7 year old Havanese. She feeds him whatever garbage is cheapest at the store, which I’m aware definitely affects his gut. My grandma isn’t doing well as so she and her dog are living at my house for at least a few months. I’ve purchased better quality dog food but I can’t stand the dog constantly having little bits of poop on his butt. I have a 5 and 3 year old that I have to wipe their asses and adding a dog to the list of asses to wipe is stressing me out. The dog will also try to bite me every time which doesn’t help. The dog’s fur is currently pretty short.

What can I do here to help my own sanity?? Thank you!