As a parent, you should be doing the same for your children - protecting their innocence. You must protect what goes into their young minds. If a movie or activity is not appropriate for them, YOU as the adult and parent need to make the decision to not allow them to view or participate. A violent or sexual image can be embedded in their mind causing all kinds of issues. It could quite possibly cause things like trouble sleeping, acting out or worse.
Don't give a child the freedom to choose whether or not to watch something...you make that decision because it is your responsibility. There is a reason that some movies are rated PG13...it means "parental guidance". Don't fool yourself into thinking that just because you attend with them or watch it with them makes it all okay. You have no idea what kind of trouble you could be causing for your child. If you are the type of parent that uses these as teaching opportunities, I can see where that could possibly make sense to you. Just be careful... Protect those that are put in your charge...they aren't prepared or ready to protect themselves yet.
Jesus loved children...He never wanted anyone to keep them away from Him. If He cannot view or participate in what you are doing...why would you think your child should? Make wise choices for them...they will be making choices for their own children someday.