Individuals entering under the Visa Waiver Program are generally subject to B-1/B-2 rules
AFAIK the parent can't be breaching their visa rules in this case but their child might. Or they might not.
Look at the Nonimmigrants: Who Can Study? table which says in a footnote for "K-12 allowed for minor children"
In some cases, a B-2 child is allowed to study if accompanying a parent and the study is incidental to the reason for the parent traveling to the United States. For example, missionaries may enter as a B-2 and the children may attend K-12 school while the parent is pursuing the primary purpose of the visit. The length of stay will not be extended to allow a minor child to complete a school year.
There's also under Visitor Visa allowed:
enrollment in a short recreational course of study, not for credit toward a degree
Your case is probably extremely difficult to decide and if you or your child gets in trouble probably needs a (very good) lawyer. In my very humble opinion, and understand I am not an immigration official and do not even pretend to be one, the shortness of your stay excludes getting any credit for said study and as such, it is perhaps allowed under the Visitor Visa rules as a "recreational course". Especially so if the purpose of the trip is demonstrably not attending this school.
Since it is 2017 in the USA, I must add that the color of your skin and your religion probably plays a huge role: if you are brown and Muslim and someone reports you to ICE you might get in trouble. If you are a White Christian the chances of trouble is extremely low.