It would be irrational to mandate a vaccine for teachers and students under the banner of COVID prevention, since the COVID vaccines aren't designed to prevent transmission of SARS-CoV-2. 100% vaccination will NOT prevent transmission.
If the petitioner is concerned about the safety of her child, she has bigger things to worry about than COVID (murder, human trafficking, depression, drug addiction, digital addiction, to name just a few). None of her fellow Virginians should be forced into medical interventions against our choosing to make her feel more comfortable.
Not only is this an irrational approach scientifically, though. It's illiberal. That is, to force such actions on Americans isn't in the power of their government. As such we're no longer discussing just a public safety issue, but a democratic freedom issue.
We cannot accept such impositions as free Americans. If we individually accept the scientific benefits of the vaccines, we have or will get them. Regardless, this "mandate" is to be opposed by any free American.
One alternative is simply to pull our kids from the leftist-controlled public school system. Assign us our share of public school funding for use at the better-performing open schools of our choice.