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I'm not sure why your vet wants to change the diet. I don't typically change the diet in my IVDD dogs. I'll treat them with anti-inflammatory meds (Rimadyl or Prednisone) and other pain meds (Tramadol or Gabapentin). I don't change their diet. I would probably just keep giving his Science diet like you were doing. If he were vomiting, then I do a bland diet. In that case, a 14 lb dog would likely get ~ 1/2 cup 2-3 times daily. I don't think it's necessary here, though.
I hope this helps, let me know if you have any other questions.
Yes, keeping him from jumping is very important. I know this is the hardest part. If needed, I will occasionally add Acepromazine. This is a sedative to keep them down in the more active dogs.