This has been the interpretation put upon Letizia walking in front of the threesome back-and-forth. However, it is clear that Letizia walks back-and-forth for quite other reasons than Sofia being with the children. I'm not sure why it keeps getting repeated that Letizia was trying to stop the picture? Can anyone explain?
BTW I notice that a common action from the adults is to touch the hair of the girls. This may be a nervous gesture (like a woman touching her own hair), or it could be a way of getting the child's full attention when about to give them instructions, though it may also be a comforting gesture for the girls (they do seem to expect it and glow when so touched).
I don't see it as controlling in the least, and both Sofia and Letizia (and I think Felipe) do this gesture.