My kids both figured out how to thwart the shopping cart straps really early. Even when I buckled it on them fairly high on their chest, and reasonably tight, they each figured out how to loosen it, then stand straight up inside of it. They could each do it in the wink of an eye, then wind up standing with their feet inside the loop made by the strap - I had Talia almost take a header because she was tangled in the strap. After a few times, I determined that the straps were practically worthless. They increased my kid's safety by only a tiny margin because they were thwarted so quickly and effortlessly, and that margin was made even slimmer by the danger they posed in tripping. That super-slim margin just wasn't worth hearing them scream when they didn't want the strap on. Whether they're strapped or not, I have to keep an eagle eye on them when they're in a climbing-out kind of mood. Strap or not, if I can keep them reasonably occupied, they're pretty safe.
For a while, I was using a home-made five-point strap, and that worked well; but not all carts were conducive to it. They didn't all have a place where portions of the strap could slip through. I failed to properly finish the strap ends (lazy...), so when it frayed, I gave up on it. But, I think something like that is a quick and easy first step that anybody can take on their own. It required a few feet of webbing and two parachute clips from Joann Fabric.
I *hate* the cars. Again, the girls thwart the buckles on them pretty effortlessly. And, they're so far away from me when I'm pushing the cart that I can't prevent them playing inappropriately - trying to climb out the front window of the car, dragging their hands on the ground. I can't always see when they grab things off the shelves we pass. Not to mention, the things steer like mack trucks and you can't see the front of it - I've accidentally run it into people's ankles because I couldn't tell where the front of it was.
I can still sling one or the other, usually Anika who's smaller. But, I can't sling both of them. Slings just aren't an option for folks with multiple kids - or many grandparents, or people with physical issues that prevent slinging. Further, Talia went through a phase between about a year and 18 months where she would *not* ride in the sling when she wanted down - and stores were a big one for wanting down.
I'm partial to the carts that have the big seats at the back end of the cart (the end where you push). The kids can scramble in and out easily and safely, when they're sitting in it they're close enough to be in my control, it's less inviting to inappropriate play. The only problem with them is they're even more difficult to steer than the cars.
I do let the girls ride on the outside of the cart, but only on the front or back - never on the sides, which makes them tip. Ani is allowed in the back of the cart, where I'm holding on, so I can hold over top of her hands so she won't fall. Tali can ride on the front, but may not wiggle it or drag her feet. Seriously, she behaves better in that situation, where she feels like she has some control over what she's doing and that she's being responsible by following rules, than she is when I deposit her in the cart seat for safekeeping. She's tipped the cart already struggling to get out of it, and it wasn't even in a temper tantrum, it was just trying to get her knees dislodged.
I have a huge Valley Speeder
wagon. It's tempting to buy one of the optional bench seats for it, and bring that along for grocery shopping, except the thing is a bear to get in and out of the car. I just wish the bench seat would attach at the front intead of the back, so the kids couldn't kick the groceries... What am I saying? DH is a woodworker! I should make him make me one! He can make it with seat belts, too... oh, now my mind is clicking away
Anyway, I think something like that would be ideal. The seats are low to the ground, low enough that, if you don't strap the kids, they can get in and out freely and safely. And wagons are much safer in the store, since you're dragging them rather than pushing them out four feet ahead of you as you turn blind corners.
Hm.... or maybe I should buy them each a pair of Wheelie shoes, and tie them to my waist with leashes. I bet they'd both love to be pulled around the store after me like they're jet-skiing