Instead of requiring that my kids had to hold my hand in a parking lot, I would park near a cart and put some kids in right away, or tell them to hold on to the cart (a.k.a. "help me push", so a kid can be between me and the cart). And they didn't have to hold a hand. There weren't enough hands. I'd say "Hold on to something," and it might be my jacket, or the strap of the sling, or the backpack, or something.
I've seen other people's children run away from them in parking lots, and the parents yell and threaten. At that moment, going back to the mom seems the most dangerous option.
Make yourself your child's safest place in the world, and many of your old concerns will just disappear.
photo by Sandra, on Diwali, in Bangalore