The pottery wheel can be funned relaxing, but like any learned skill, it takes time to learn and master.
If you are first getting into ceramics, I always recommend doing a hand building class first. You usually want to know how to walk before you can run efficiently.
Kids who are younger than 10 have struggled A LOT during the class and have had a REALLY hard time keeping up. This is why we no longer have kids younger than 10 join the classes. If you would like a private class you can book all 6 wheels for $270 and your child who is younger than 10, and they can have the 1.5 hrs of private lesson time solely focused on them. Otherwise, pottery class requirements are MATURE 10 and older.
In my experience, the pottery wheel class is not recommended for birthday parties as it is an instructional class... who wants to be lectured for 45 minutes at a party!