I usually send them home and invite other animals to visit my campsite. But yes if you send them home, you will see them appearing again and asking requests. I wonder if AC will come with an upgrade for animals which has reached level 20, but I am not sure if they will do anything about that.
I have 20 something at max... There will be times when your rotations will be four people all at max. At that point it's up to you if the money/resources are worth filling their requests. If you want pictures, though, you're gonna have to keep shifting animals through your campsite when they max out. It'll be worth it even though they show up in rotations!