For what it's worth...

(I'm a super-newbie)
I am running Mame32 through Mamewah (not recommended, I know), and I can tell you two things...
First, if I should try to shut down the computer using the front power button while actually playing a game (I tried this playing Dig-Dug under Mame32, and a pinball game under VPinMame,) I will get the end program and then the subsequent program not responding dialog for Mamewah. If I then click "end now" or whatever it is, I get a clean shutdown.
However, and more to the point perhaps, if I am actually in Mamewah, i.e. at the menu to select a game, and I press the front power button, everything shuts down just fine.
Looking back at that, it seems like a lot of commas.
But anyway, it seems the easiest way to get around this problem is to shut-down when in Mamewah, and not actually in a game. I gather from re-reading your first post Arcaic that you or your family are shutting down from within a game.
Actually, the more I think about it (I've had a few tonight), I haven't really helped at all, except to say that (I think) I can duplicate what is happening to you. But could it be possible to train the wife and kids to get back to the Mamewah selection screen before hitting the shutdown button?