I give up ..acoustic treatment for room with vinyl plank flooring

+1 for Primacoustic panels. I treated all four walls and the ceiling in a dedicated listening room. Biggest improvement in SQ. Much bigger than any gear change. Place at all first reflection points, plus additional coverage on front wall (the wall behind the speakers) and the back wall (the wall behind you). Ordered mine from Sweetwater sound. No affiliation, just a happy camper.
Tom

I agree with Erik.Forgo the rug for now and treat the ceiling along with any wall/corner treatment.GIK will consult with you for free.
As a certifiable dog geek, the most effective way to train any animal is by the four quadrants of operant conditioning.And yes,many of the small dog breeds are almost impossible.If it were me I would train him to go indoors on a pee pad.I've trained and competed with dogs for years so I know a little about it.Your little guy will want to return to that same spot if he can smell the tiniest whiff of urine.The very best enzyme cleaner I've found is Kleen-Free,available online.Good luck!

There are also these strange things called curtains.