You HAVE to be consistent here. That means, he doesn't get to walk in the store one day and have to ride in the cart the next. I have a 3yo son and in my opinion behaves very well but letting him walk in a grocery store/Target/Costco, etc.. is sort of setting him up to fail. Just too much to look at and do. So, since day one, he has either been on my back in my Ergo Baby carrier or in the cart (with a floppy seat so it is nice and comfy). I always have a drink and a snack or two and I have never asked him to ride in the cart. I just put him there and there he goes. He has asked if he could walk and instead of saying no. I say something like,"you want to walk? that would be fun, but Mommy has a lot of things to get and it just isn't safe, maybe sometime when we are just getting one thing, we can walk, OK?" When we shop at Trader Joes, we go straight for the fruit snacks and he picks one out. Sometimes, I now let him walk if we just have one or two things to grab at Target or even the store but it just depends on the time of day, his mood, my mood, etc..Also, I don't take him shopping if he is tired or hungry unless I know he'll crash comfortably in the cart or bring food/drink if he is hungry.
Sorry, that was way too wordy but I can't make it shorter now! LOL. Make the cart comfortable (get a floppy seat if you don't already have one), always have something to eat/drink, bring a toy, maybe a notepad and crayon for him to scribble on, and redirect as much as possible. As soon as you pull the cart to the side of the car and he starts to panic, just talk to him and tell him the plans. We are grocery shopping and I need you to sit in the cart so you can help me, today I need you to tell me when you see the apples, or ?? Whatever works. You CAN run errands with him during the day and get your nights back!
P.S. I just read the other responses and although I think having groceries delivered sounds wonderful, it is a great place for kids to learn about food. Grocery shopping can be FUN! It's actually one of my favoriet things to do with my kids. They learn what grow food is and what junk food is. They can have some control and help pick out a cereal, veggie or fruit, etc.. You can do it! (-:
Best of luck,
M.