I am a childless female 20-something who occasionally comes in to contact with other people's children. This happens anywhere really, at work, stores, museums, movie theatres, just around the neighborhood. And sometimes these children are being rude. I tend to be very forgiving about things like someone bumping into me accidentally and will say "No, no, it's fine." But when someone does something like cut in line or talk during a movie I will ask them not to. With adults I feel comfortable doing so, but when it is a child or young teenager I am not sure if it is appropriate/how the parent may react.
For this question I will limit it to when the parent is there and does nothing.
For example, I was in a museum using an interactive exhibit when a child squeezed into the small gap between me and the exhibit, pushing me out of the way to use it themselves. Their parent was only three feet away and watched this happen without saying anything. I wanted to tell the child something like "Excuse me but I was using this, would you mind waiting your turn?" but I was concerned about the parent reacting negatively to me correcting their child so I walked away.
In these situations I am mostly worried about the parent. When it is just me and the child I usually say something and as long as I am gentle and polite the child seems to understand and correct their behavior. But I have seen parents go nuts when someone says anything remotely corrective to their children.
In such a situation should I say something the child or the parent? Is there a particular way I should phrase it?
It seems wrong to just let such things happen and not say anything. I wouldn't let that fly with an adult so why should I let it go with a child?
EDIT: To add some clarification I am in the US. And the age range I had in mind was 6-13. That seems to be when they are still oblivious to their surroundings but old enough to understand if I were to say something.
The answers seem divided on whether or not to direct the comment to the parent or child. Both sides make good points so I am still unsure which would be best. It seems like in the majority of cases speaking to the child would be alright but in the minority of situations where the child has behavioral issues it could easily go wrong. If this isn't resolved in the answers I might make a new question about that specific case.