Our cat gets smothered in love, but from very early on DD mastered the concept of gentle. I taught it to her using exaggerated body language & facial expressions - seems to get the message through more than just the words. It's also worth modeling concepts around gentleness & respecting space when the kids are playing with other kids.

We have a tv cabinet (old school, I know) and we've placed it at an angle in a corner of the lounge with just enough of a gap on both sides for the cat to go behind into the triangle shaped space. Cats like triangles . Maybe you could do something similar with a lounge chair. It doesn't need to be a big space, just a hidey hole with an entrance and an exit. We also have our lounge in front of the window so the cat can sit on the window sill in relative P&Q.