If a burglar opened the shutter and windows from outside, causing Madeleine to wake and flee she wouldn't have fled via the front door because that was heading towards the perpetrators. If she fled out of the patio doors then her mother was wrong; she did close the gates behind herself. Assuming that Kate was correct when she said both gates were closed when she arrived. So why did the children's bedroom door move between 8.30 and 9.05? Why did it move again between 9.05 and 9.30?
What is slowly dawning on me is that there could be period between Madeleine being woken and when she leaves.
I'm tending to think like this now:
1. The burglar opens the window and raised shutter prior to Matt's visit.
2. The noise woke Madeleine who then went and hid in the apartment.
3. She hears Matt coming in the apartment and later leaving via the patio door. (Since Madeleine doesn't really know Matt she treats him as an "intruder".)
4. Since the "intruder" left by the patio door, Madeleine plucks up courage to leave by the front door.
It is possible that Madeleine had a tendency to hide if she was frightened and it was the reason Kate did her search in the apartment once she noted Madeleine not in her bed. What I am saying above is closely related to what Kate felt initially.