They can attend with some precautionary restrictions from haram behaviour as you have mentioned.
Ayatullah Sistani says the following:
"It is permissible for adults as well as children to learn the art of halãl music in music schools or other places as long as their visits to such places do not have any negative effect on their proper upbringing."
Addition to this we called the office of Ayatullah Sistani and their reply to the question was as follows:
Agha's emphasis is to avoid all destructive haram temptation kind of things in this process. I.e. the child should not get mesmerised into the learning and enjoy it. The child should be aware of why and how he should be attending the class.
In short because it is a forceful act then the child should be in the classes as if they are not in the class.
Ask an Alim team.