Mine do the same filling of the cart. But I have my two carts and baby stroller out all the time time, so there is no novelty to them when they are played with - but I have the space as I have an upstairs and downstairs playroom. I always have the rule that whatever is in one's cart is "their turn" to use and no one can touch the stuff. If a toy is fought over I usually just take it away. But if one child has too much stuff I will clear some of it out and share it more evenly with the other kids.

I don't do the hula hoop things, so can't comment on that. I don't limit where the children can play, and will just step in and remind that it is not their turn if another child tries to take a toy from someone else.