30+ years ago when I was in high school, we had a Civics class that taught us how our government works and what our Rights are as citizens.  The one thing that really stuck with me from that class, and has served me well ever since, was when the teacher summarized a lesson on the limits on Rights with the following principle.

"Your Rights end, where my Rights begin."

Assuming that the original poster has the "Right" to send their children to school that "Right" does not supersede my "Right" to determine the medical treatments that I and my children receive.

There are many reasons that people do not want to get the COVID-19 vaccine.  I find it troubling that instead of respecting and addressing these reasons, that more and more our Government, at all levels and through multiple departments, are trying to force compliance through indirect means. 

Since the beginning, the medical field has told us that the risks to unvaccinated children from COVID-19 are minimal.  If someone decides that it is best for their child to be vaccinated on top of that, that is their Right.  If the vaccine is as effective as all the companies have been advertising, then the risk to a vaccinated child from COVID-19 should be infinitesimal.  Why should you force other children to be vaccinated as well?  What is the gain?  And why should that allow you to override my and my child's Rights by forcing us to undergo a medical procedure?

I also find it problematic that this proposal does not include traditional exclusions for medical and religious reasons.  Do these not matter any more?  

And why should this apply to private schools as well as public?  The Government certainly has more leeway in determining requirements for public school programs that they are responsible for, but why should this apply to private schools?  Parents are free to decide if their children go to private school instead of public schools and they pay for it themselves.  Let the private schools decide their own policy and let parents decide if they like them or not.

So, NO.  Do NOT mandate COVID-19 vaccines for all children in school.  Let me decide what is appropriate for my child - vaccine or no, go to school or no.