When I take all 4 kids shopping I almost always bring the triple stroller. Occasionally I've done it without the 3rd seat, but not on purpose!! Brianna sits in the 3rd seat (front) about 99% of the time because 1- she'll sit up the entire time, and 2- she doesn't chew on the front bar of it :) And those would be what Emma and Micah do when they sit there... for very short periods of time.
Kristopher is great and he walks with me or rides in the basket of the cart until there's no room for him to sit well in there. I usually get him involved and ask him to get specific things or I'll hand him things to put in the cart. He likes helping and it gives him something to do so he's not just wandering around with us and bored.
If I only have Emma with me, as I occasionally did during the school year when the other 3 were at the church, I would push her in her wheelchair. Unfortunately, the new wheelchair is a little harder to steer with one hand... but it's ok, I can throw a foot or elbow in there on occasion and we make it work!
I always push the stroller or wheelchair and pull the cart. We might look like a parade, but my kids behave wonderfully at the store and like being out and about! Sometimes I will go after the kids have had dinner, or even after bed, if I wasn't up to it (or have time for it) during the day and we need groceries. Those trips are about 30 min shorter, on average, and I don't get home quite as exhausted, but since the kids are always so good when we go as a family I think it's a good experience for them to continue to have.
I'm sure once school starts I will be grocery shopping while the kids are at school most of the time, so we'll enjoy these outings while we have the chance to make them!
PS On the rare occasion that we ALL go out to grocery shop or to stores, we usually bring just the triple and one of us takes the cart, the other the stroller, but if we're going to be walking around at a mall or outdoor shopping center, we often bring the stroller and wheelchair because it allows everyone a better 'view' and also lets us split up the kids between us a little more if we're trying to feed them or whatever :)