this is something I deal with all the time- and actually spoke with my sons therapist- she said to not take him and use it as a privelage. so for now no more taking him-
if he was smaller I would give him instructions before going in- I would let him know that we are going in here these are the kind of behaviors expected of course word it in their language- they do not need to have a tangible reward- a hug a high 5 or good job at the end of the shopping goes farther then you expect
as far as people staring- hmm well that is something I had to deal with and still do- I ignore it- and keep going with what I need to do- they do not live in your household so they really do not understand what you are going through- I carry my sons paperwork with me of times where he was baker acted and shows that he is in therapy just in case anything is questioned.
If you have a therapist or a behavioral specialist at your childs school contact them - they are very useful resources