K.P.
My children are 3 and 5 and I deal with this every time I go to the store. The younger one is my problem. He then feeds his sister and makes her misbehave. I have started leaving one of them home with my husband when possible. I have actually told my son that until he learns to behave at the store, he will not be going. My daughter learned early that I am not going to put up with it. Apparently I lightened up with my son without realizing it.
Maybe it's a boy thing. I have tried one walking on each side of the cart. That works for about 10 minutes. I put him in "time out" where he has to sit in the cart while I shop. Then I look like the crazy woman too because all he wants to do is cry and I tell him to go ahead that it doesn't bother me.
He is slowly learning and getting better. Boy do I stress SLOWLY. If I take him by himself, he is generally good as gold with the typical 3 year old Mommy can I get this, Mommy can I get that.