In your theory did Madeleine get up before 9:10 then go back to bed and settle herself to sleep again after waking up alone in a strange place/country?
If the bedroom door was wider open at 21:10 than at 20:30, then it can only have been the child who made it wider open by leaving the bedroom then returning to the bedroom, for example to go bathroom, or to see if adults are in. I don't think this return trip, if it happened, is of any importance.
I am interested in the door becoming wider open
after 21:10, which IMO definitely did happen, and it can only have been the child who opened it, to go into another room, I have already explained the reason for this, which is someone opening the window and shutter from outside.
The key fact (or assumption you might say), which is required to be recognised to understand this short sequence of events, is that the apartment looked like no-one was in. If I got that wrong, then my whole theory (and I only posted the first bit) is nothing more than a pile of horse droppings.