What can a non primary parent do when the primary parent allows children to go to public entertainment centers unattended?

Answer 1

Legally unless these "public entertainment centers" drug dens and brothels there isn't anything that you can do.

If you can prove that by doing so the "primary", such an ugly word, is endangering them unreasonably take them to court. If your are simple grasping at straws trying to get the other in trouble don't bother.

Also the child's age would hae more to do with it than anything.  I see no problem dropping a 12-13 year old off at the movies with ot without their friends and coming back when it was over or watching a different flick at the same time.