Oh, I understand that push bar setup. But there is a feature to them, often, that maybe you and daughter aren't familiar with. The mechanism to open the door with a push, on a push bar, can be disabled with some sort of locking mechanism. For security purposes in a commercial building, you don't want your premises accessible as easily as someone bashing a hole and pushing the bar, so this is the answer to that problem.
In fact, they have such a setup on the doors at my church. You can push the push bars to get out, during hours they are open. But after hours, according to a timer set by a system setup, all those push bars become disabled, and you can go to a door and push, but it won't disengage the lock to allow the door to open.
In addition, if we consider the damage to the kitchen door, it suggests that the push bar there had been disabled in such a manner. The perp smashed the window, but apparently that smash-reach-push did no good, and it appears he had to pry off the lock itself in order to be able to get in.
That might also suggest our perp was someone who wasn't a burglar who knew what to expect with such a door, or at least not a very experienced one. He might have been like your daughter, who only knew that every time the bar is pushed, the door opens. But, not being aware that if in the building after hours, it won't.
