Odd, I thought the non-AVOD films were edited. I definitely remember seeing Bridget Jones from IST to LHR years ago that dubbed over the swear words. And I don't remember ever seeing violent films on the overheads either.
As for the AVODs. Tell the kids to exercise manners and not be watching other peoples screens.

Besides whose screens are they seeing anyhow? Aren't their parents sitting next to them?
I will say though I have felt uncomfortable at times watching movies on my laptop. I remember closing the case a few times during more violent parts of Band of Brothers but I was on the aisle and had no idea who might be over my shoulder watching since this was before the days of AVOD in coach.