Unless they are severely underweight, I would not restrict exercise b/c they eat less when playing. They may actually be overeating out of boredom when restricted to their cage.
Screaming when simply being picked up suggests either they were badly abused in the past, or you aren’t picking them up correctly. Bunnies very very rarely scream, they are mostly silent. I’ve only heard a rabbit scream twice, and it was under extreme circumstances. So, even though disliking being picked up is normal for a bunny, screaming is highly unusual, and mild discomfort shouldn’t lead to it.
If you are picking them up by the ears or scruff, that would be hurting them, or if you are grabbing at their feet that would hurt them. Basically if you’re not sure if you are picking them up correctly, you should check out some instructions for handling them.
If the problem is that they have been deeply traumatized by an abusive past, it’s going to be much harder to fix. It’s just going to take a lot of time and patience.
I wouldn’t worry too much about daily grooming on a short haired bunny, they don’t get blockages that easily, just make sure they get lots of fiber.