Are you leaving the wet out all day?
If they are eating some and then stop, it sounds like they are playing you. And it worked because they got the dry food they wanted.
Put down wet for 20 minutes and then take it up, cover it and put it in the fridge. Then put it back down later.
Sometimes they do, and that's usually because of higher protein, but here is the catch:
The kitten version of say, Cat Chow, would have more protein than the adult Cat Chow, but wouldn't have more protein than Solid Gold adult food. So if you were trying to get high protein, the kitten version...
Well, for one I can ease your worries by saying you do not need to switch from 'kitten' food to 'adult' food. They are just marketing ploys and not much else.
I agree with others that the dry food is most likely the culprit for your boy's tummy issues. Dry food is just really hard on cats...
What kind of renal diet is it?
Dry or wet?
Here is an article that will be very helpful for you, I think.
(Title says dog but article talks about cats as well)