G.B.
Hi K., I am a foster/adopt mom. Maybe try using choices and only positive words. If you say "no", or "don't" his first instinct will be to run, it is a game for him. Try to say, "when you come back by mommy, we can go to A or B. " Let him know that he has rewards for behaving when you go out. Talk to him on the car ride to your destination about where you are going, what you need to do, and what he needs to do. Make sure that you keep it simple, he is young, but he understands. Tell him that it is his job to hold your hand, or stay in the cart. That way he knows what is expected of him. Then tell him what his rewards will be if he behaves. Perhaps extra time with mommy reading his fave book, or bubbles in the bathtub. Use the reward as a reminder while you are out and praise him ALOT when he is being good. Hope this helps.
G.