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I use the reward and punishment in a different way. I let the kids know in advance, as soon as there is the slightest indication of getting out of control the good stuff is over - even if we are on the way there or in the parking lot. And I give them 1 warning to calm down and tell them what the consequences will be (ending the trip immediately) if they do not. And then I follow through with it. I don't beg, plead, and give chance after chance. After the first couple of times of following through they cry about it and I turn up the music on the way home. Once home, we discuss it. I remind them that this is a consequence of their own making and the next time they will want to make a better choice. I ask them what that choice would be. Then we do something nice on a much smaller scale.
If they still act up the next time out the consequences end up being staying at home without something nice. Eventually they will learn to behave themselves in public because the reward is doing something wonderful!
Start with good behavior at home and shopping. Then let them know the reward for the good behavior will be to do something fun as long as the good behavior continues. Let them learn to apologize for their bad behavior and encourage them to work on good behavior. Making excuses because of a disability is equivilent to teaching them that it's ok to misbehave where ever they go and no matter what their age is.