You're right, "Shall we" is not generally used by Americans as a tag question. However, we do use "right" at the end of a sentence for all ages but not in the way that "right" is so frequently used in the UK. For example, an American regardless of age could say, "we're going home, right?" when seeking confirmation regarding what will happen. In your example with the child, the adult is seeking confirmation from the child that the latter knows that punching a sibling is not acceptable. Thus, "right,?" and "is it,?" in these contexts confirm/underscore what the other person (child) already knows. Yet when I hear Brits use, "right" a lot at the end of a sentence, it seems to me to be a declarative statement, not a question. "We're not revisiting the issue. Right. Now what else is on the agenda?" "Right" ends a topic and the speaker moves on.
In the US, I think a common tag is "OK" for people of all ages and is used both in a declarative way and in a questioning way. For example, "I don't want to go over this again, ok? You're not to use my computer!" "You need to wash your hands before coming to the dinner table, ok?" ("Right" and "is it" don't work in these examples.) One could also hear, "you're not to punch your little sister, ok?" The adult isn't asking the child's opinion of the punching but is stating that it is not to be repeated.
The trouble with OK? is that it can sound as if one is asking the other person's permission so parents have been advised not to use it as a tag. Still, a lot of people in the US use, if not overuse, "OK?" Foreigners do need to understand what the tags mean but I'd be cautious about using the expressions without LOTS of exposure in context since there are many nuances -- e.g., tone, social context -- that affect how appropriate they are in a given situation.