I don't agree with all the anger and hate you are getting, although, I also I don't agree with moving your children school as the upheaval might be really damaging for them.
However, if you are struggling with perimenopause and this woman has been keeping a 'care package' in your/your husband's car for the short journey to school, I think that's a massive overstep and really weird thing to do, so I can see why this has made you feel paranoid. Perimenopause/ menopause can definitely heighten those feelings.
The key issue here is that your husband has ignored your feelings on this matter. He continued giving lifts and allowed her to keep this 'care package' in your car. You and your partner should be a team. Whilst I don't agree anyone can tell their partner who they can/can't be friends with, I can see why your feelings are hurt. Why is he allowing it?
If nothing else, he could have cut lifts and not let her leave the care package. Your husband, for whatever reason, hasn't tried to respect your feelings and has enabled the woman to cross boundaries. That's the key issue which I do understand why it would make you feel like this.
I think you perhaps need to evaluate what you need from your husband and whether he will engage with you about the issues.
If you genuinely believe this school will be better for your children, then that's one thing but please consider that it could be very upsetting for them and it's not dealing with the actual problem.
My husband used to get fawned over at the school gate for various reasons, there was one woman he helped once with her bike puncture and she would ignore me completely and, in front of me, flirt with him, try to touch his arm, ask him out for coffee etc. He was oblivious and thought she was just being friendly, even when our friends mentioned it. It grated on me but she hadn't done anything 'wrong' so I stood there seething. I did tell him how it made me feel but he thought I was being a bit silly. One day as we were collecting DD from school, she caught sight of him and physically elbowed me out of the way to get to him as I was trying to deal with DD. He saw her behaviour then and why I was upset, it was so bonkers, I still re-live it in my mind sometimes. He was really firm and shut her down from then on and apologised to me profusely. Do you think your husband is the same? Potentially not seeing the issues you are as he sees her as harmless?
Either way, until you deal with the actual problem you're just kicking the can down the road for another time. Changing schools won't help that.