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

There are also these strange things called curtains.

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!

+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

Primacoustic room treatment. Calculate surface area of walls. Use 2" Broadway panels equal to 15% of of surface area of side walls for a lively room result. Use 25% for a well dampened room. 20% will give you a middle result. You can ceiling mount or wall mount with the right hardware options. The biggest factor is having enough dampening material/panels. However, for that last few percent of performance use the live wall, dead wall approach with the speakers on the dead wall... For the live wall you can use diffusers or an array of 1" thick 12"x12" scatter blocks. Check out the London room kits for examples. There are fabric options or a Paintable/printable panel option. Check out www.primacoustic.com

While I do have an area rug on the floor in my new listening room, I also have panels on the walls.  In the past I also had to make sure the curtains were closed for the best sound. 😁

All the best.

JD

Compensate with extra ceiling treatment.

pee pads

The thing with dogs is to scold them when they do wrong and tug on the choke chain (not yank) while training them. Immediately after show the dog some love. After a few times he'll recognize that that particular behavior is wrong and that you still love him. That way, he'll gladly stop doing the "bad" thing.

And, don't worry about tugging on the choke chain as the structure of a dogs neck is the strongest part of his body.  I forget the name behind the procedure but that's how they've been training dogs in the movies for decades and how I trained my Rhodesian Ridgeback/Lab mix. 

People would marvel as when I stopped walking, he'd sit, and wouldn't move until I asked him to with the proper command. I'd have strangers pull on his leash and he wouldn't budge. 

All the best,
Nonoise

Another vote for treat the dog not the room.

No George.....not that way

I love animals, and also thought it cruel, but it was the only way in the end in my case with one of my pets, I tried everything, as has the OP.

Cheers George

This actually works well .
the reason for the bad reviews IMO is because you must claen the carpet or rug to remove pee smell and stain before using this .
You cannot just spray it on top of pee stains.
https://www.amazon.com/Pet-Organics-Nala-DNB04016-Housebreaking/dp/B003NTJ8QW/ref=sr_1_4?gclid=EAIaIQobChMI37LP0KrX5AIVgoTICh2nbgXvEAAYASAAEgLSCfD_BwE&hvadid=295397789958&hvdev=c&hvlocphy=9013450&hvnetw=g&hvpos=1t1&hvqmt=e&hvrand=3789553785891702931&hvtargid=aud-647006051489%3Akwd-571129334610&hydadcr=15974_9507381&keywords=dog+stop+pee+spray&qid=1568705304&sr=8-4

No George.....not that way

Contact GIK.  They will help.  I’m guessing some 244 panels at all first reflection points.  Ceiling, side walls, center of the front and back walls.  You might consider buying 2 extra ones that you can just move onto the floor in front of the speakers when you are really listening.

My grandma always rubbed the dogs nose it it which works well.  They must hate the smell of their own piss all over there nose, lol.

I’m an animal lover... maybe your dog just gets really excited to be listening to music with you 😁

Ok so I have a small dog that for the life of me cannot stop from pissing on my area rug in my listening room.

If all else fails the only way to stop this, is be hard and to immediately rub his nose in it and put him wherever it is you want him to do it, he will "get it" after a few of times

Cheers George

I use a bamboo rug (felt backing) over a slate floor & like it better (sound wise) than the wool (blend) rug I had previously. Not sure how your dog will like it though.