To expand a bit on my last post, if you HE in the long run your daughter will inevitably end up coming along with you to places she might not have chosen to go and where you might not have chosen to take her. They will often be places which aren't designed with her needs specifically in mind.
This experience is often rather a pain in the neck. It can be embarrassing to be the only parent around who has an older child and I find myself wishing my dd would be perfectly helpful and outgoing. That expectation isn't fair to her. In my opinion she should be allowed to participate (or not) on her own terms, provided she isn't severely bothering others.
This may be difficult at the time, but there can be a value to it as well. It may take a while for that value to become apparent. You might discover that once your daughter has been coming along a number of times, she begins to be more comfortable and starts trying out different ways of behaving and maybe even interacting with people. Or you may find that once they have got used to her, other people accept her for who she is and become more tolerant. Or both.
There are skills your daughter will be learning when she goes places with you. I used to feel a bit sorry for my daughter because she had to trek round shops like Tesco so often. Educationally it seemed a waste of time, and she didn't enjoy it. Then one day as I parked, I was grumbling about having to haul her crabby little sister round the shop. "You two can sit in the car and read the library books," she said. "I'll do the shopping." I handed over the list and money and off she went. Now we do that often. She loves to shop now that she has the responsibility of it.
As I said, if the experience doesn't seem to be working out then cut your losses and stop taking her. However, it sounds like it is OKish at the moment, and in the long run it might turn out to be quite all right.