K.O.
Well, I do an in-home daycare and I watch a family that has 4 children. 2 of them are in Elementary school all day and 1 goes to a college preschool when the Mom goes to school. So, on those days, I only have their 1 child who is almost 2 years old. I consider him like he is one of my own and I do take him on errands and to/from school to get the other kids.
I think it is about having a relationship with your provider. I am great friends now with the parent and love her children! If you are uncomfortable, maybe you should talk with her and let her know how you feel and what can she do or say to make you more secure.
Also, I would make sure that she has the right kind/size carseat for your child. Ask her what her plans are if she has to get out of the car for any reason at the school. Tell her that you DO NOT APPROVE of your child ever being left alone...even for 2 seconds. She might put your mind at ease. If not, you might have to find yourself another sitter.
I guess, my belief is that if you trust this person with your child in your home, why would the trust be any less going to and from school?
Good luck. I hope I helped in some way.