I am going to be facing this at some point.
need to find someone with legal competence in your state with an interest in this topic to opine. you may have options. I would be very careful with any further correspondence with your employer in the meantime - you may have closed some possible avenues with your initial answers.
If I was earlier in life and had kids depending on me, though, I would be tempted to take the vaccine as "just another sacrifice for the kids".