Does anyone know how to find out if your child is banned from Xbox live?

For a communication ban there is normally a message sent either to the email or via xbox messaging to the gamertag.

Usually when a comm band happens enforcement sends out a notification two a few places. One would be the email address associated with the gamertag and they send a message to the xbox itself under that particular gamertag. Check there to see if there are
any messages.

Visit: https://enforcement.xbox.com/en-us for more information. Or have your child sign in and a message will pop up detailing why he was banned.

Hello ConcerneddadLP,

Thank you for posting on Xbox Forums. In regards to this issue, if you are inquiring about your son's possible enforcement action you can do so by going to the
Enforcement Website. If you can, try to log into your child's account to see if a message about the Enforcement action comes up.

Once logged in on the website through your child's account, if you find out that your son is suspended for longer than a day you can also
submit a case reviewfrom the same website.This
is how you communicate with the enforcement team and it's the only way.

I hope this helps and thank you again for posting on Xbox Forums!

You should log into the enforcement team website for information where you can also submit a case review if the suspension is eligible.
http://enforcement.xbox.com/home