Here, our theater restricts the shows later than 8pm of R rated movies so that no small kids are allowed. (I can't remember the exact age - 10 maybe?)
I think this is a GREAT idea...if you really want your children to see an R rated movie, or just really want to see it yourself and have no option but to drag your kids along with you, then that's fine...but your butt needs to come to an early show. That way, people who want to be assured that a badly behaving child won't be in their theatre during a show can go to the late showing, and watch the movie with other adults in peace. Perfect compromise.
my theatre also has a special thing they do where the 1st matinee showing of EVERY film in the theatre on Tuesdays, is "family" showing. This means that is is expected the theatre will be packed full of toddlers, babies, kids, and they leave the lights on a little bit and tone the sound down a bit(so as not to scare small ones), and have "valet" stroller parking, LOL! Great way for mommies to get out and take the older kids to a movie or just get out themselves, with it being understood they will have a baby/toddler with them, so no glares or feeling like you are interrupting others, etc. It's a madhouse, but hey - it';s a neat option.