Just so you know, a LOT of us have second-hand dogs and we'd never refer to them as "just a pound pup"... Regardless of the pedigree, every dog deserves an equal chance at a good home and deserves having great care and love too.
The only way to fix this is to keep working with your vet to find out the cause. This is definitely not a training issue and in my opinion, no problem ever warrants removing or limiting the water supply.
If you believe in your vet, you will eventually find the reason for this and then you can work on fixing it.
Good luck.