First, the adult without the issues really shouldn't be on a prescription food. I/D shouldn't hurt but there are better choices.
If the vet was worried about the pup getting into the other dog's food, then the pup should be exclusively eating I/D (no treats of any kind). If the pup hasn't been doing well on I/D with no treats, the food does need to be switched.
What food was she on before this?
Never mind.
I see you answered my question already.
This sounds a lot like Ellie by the way.
What blood work has been done?
You can't get her back on RC?