Completely agreed. Moving the kittens around is just unsettling. Choose one space for each and keep them to it.Personally, I would have the new kitten sleep with you as Muffin is already bonded to you. It is not a good idea to move her back and forth during quarantine.
if your parents do have a baby gate, that helps. It doesn't allow you to have the door open and the kitten stay in unless you pile 2 or 3 on top of each other to completely cover the doorway, but it does slow a kitten down and then they have to jump up to what is more your hand height...saves that "strange gorilla walk" that Rafiki mentions, LOL!