So sorry you are going through this.
I think you'll find that most of us found a whole new world of things to worry about once we became parents. I also think it is common for mothers, especially, to worry about our children, and occasionally, we allow those drastic scenarios to overwhelm and hold us hostage momentarily.
The operative words being occasionally and momentarily. What you are describing here seems to be more intense, more frequent, and more pervasive than the occasional or short-lived episode. (e.g., you're becoming physically ill, on a daily basis, when you have to take your oldest to school).
And for that reason, I will say to you what I'd say to any dear friend who came to me with this: please talk to your GP or ob/gyn and get a referral to a well-qualified mental health professional to help you with this.
The good news? You've got a lot of insight into your situation, and that is the first step to getting yourself onto another path. You realize your anxiety and worry are out of proportion; you realize you can't teach your girls to be unafraid and confident when you yourself are terrified; and you realize all of this is making you physically ill in addtion to the emotional distress you're experiencing.
The other good thing is that these kinds of fears can be dealt with and managed successfully when a person is highly motivated, as you seem to be, to seek help.
You're about to make a major decision about your daughter's education. While there is nothing wrong with homeschooling, you should make that decision based on what is best for her and her needs, not because you are petrified about the outside world.
Keep coming here for support as you need, and also be sure to contact your Dr. for a referral so you can learn to manage this before it overtakes your life and begins to affect your daughters negatively.
Hope this helps.
J. F.