@audphile1
+1
As an owner of an 11 month old puppy, I can attest to the efficacy of getting in front of the problem. You start by taking her out to the same place every couple hours. Then slowly extent the time.
Second, you want to get a Bissill Pet Stain Erasure:
https://www.bestbuy.com/product/bissell-pet-stain-eraser-plus-portable-deep-cleaner-cha-cha-lime/J7JZ6T4KJ9
There are several iterations. The hand held device allows you to go and shampoo each accident when it happens. It does not have rotating brushes so you don’t have to worry about the shag.
If you want to find the exact locations of each pool, Then get and inexpensive black light. In a darkened room, with the black light, you will be able to see each problem. Remember this is temporary.
If you choose to replace the rug. then get a good sound absorbing rug with pad of what looks good to you. Training and the Pet Erasure and you will have a clean rug.
Get a private trainer to come to your home. About $100/ hour. Well worth it. She will help train you and your dog. And this will be only temporary.