Don't you dare doubt your reaction on this! I would have done exactly the same as you. As I was reading your account of it, I was thinking just that.
I think you have done exactly the right thing writing to them to tell them how upset it made you. It must be a terrifiying experience to be pursued through the town and accused by the police of shoplifting.
The store needed to be made aware of how upset you are about it - and to have it in writing as well. I would make sure you get a prompt reply too. If you have not heard anything after a few days, then you should send the email again, copying in all the relevant bodies, asking if they are yet in a position to reply.
I like to think that, given who they are, the store will do the right thing and will probably be appalled at what has happened and I would give them a chance to make it good.
Take care x