Star, I love those lines! But seriously, it is far better than slinking around looking embarrassed. That only makes the problem worse, because it sends a message to onlookers as well as difficult child, that you have a weak spot, and that you DO feel personally responsible (as if you could do anything anyway).
Something that has worked for us - we have several rules for when we are grocery shopping.
1) Never shop when hungry or thirsty. This is a standard rule for everybody because it has been shown that if you DO shop when hungry or thirsty, you impulse buy a whole lot more. And if WE do that as adults, what is it doing inside the head of a difficult child?
2) Never shop when tired. This also applies to children, especially small children. If you are breastfeeding a baby, always feed the baby somewhere quiet before you go into the supermarket. There's nothing worse than having stacked your trolley, than to have to walk out of the store and leave it, ice cream melting, to feed the baby who is screaming the ceiling down with her decibels.
3) Always get the kids needs met first. This is a rule at home as well as shopping. When they have stopped screaming at you, you will be able to think more clearly to get your other tasks done. I also enjoy my meal much more, if I've fed the kids first. If I'm pan-frying fish, for example, and I have to cook each person's meal in sequence, there's no point me trying to eat while I'm still watching a hot pan. I can enjoy my fish much more, with the sound of chomping from kids and the pan turned off.
4) To feed and water shoppers, it's cheaper to buy ingredients from a supermarket (or similar cheap place) and assemble your won somewhere pleasant, such as a corner table somewhere or in a nearby park with playground. Just about all kids will be far easier to manage if their hunger at least has been assuaged.
And now to shopping - I take a list. If a kid is being a bit of a headache I give him a small job to do. It will depend on the kid's ability and interests, but at the absolute youngest I will get a kid to get their favourite food off the shelf while I am supervising. "You like baked beans, don't you? Well choose the one you want..." (they often recognise the tin by colour, if they are too young to read) "...and give it to me and I will put it in the trolley. Thank you! You are a clever kid. And now we have your favourite baked beans!"
difficult child 3 started at this level, then I could get him to go to another aisle and find out where the strawberry jam was, for example, and come and tell me. As he got older and more capable, I could give him the shopping list and let him navigate me to the next item. Later, especially if he was getting noisy or difficult, I could get him to find out which brand and size of baked beans was the most economical (hint: we break it down to price per 100 g).
The kids are allowed ONE item each, limit $2, as a snack to eat/drink once we have paid for the product "because we mustn't eat it until it's ours to do so." I also get myself a snack under the same rules (usually a carton of milk).
Having a routine when we shop, helps. It took time, but it really works. We arrive at the mall and do incidental shopping - clothes, shoes, equipment, books - then when all else is done, we do the groceries then the fresh vegetables then we load the car and then we go home.
In the supermarket, we load the trolley as carefully as we can, so as not to crush things like bread and crisps under tinned food. We follow our list as much as possible and walk the aisles. If the kids want something, we listen, talk about it and give them a choice - if it's non-essential and nobody else will want it, the child has to pay for it with their own money (ie it comes out of the $2 snack allowance). So "I wanna pack of Twisties!" becomes, "You can have a pack of Twisties if you like, but you can't have Skittles as well because that's two things. I don't mind which you have so you can choose. If you argue about it, you will get no snack at all." I have to be careful with this one, because easy child 2/difficult child 2 especially had trouble with these decisions so I often had to talk her through making her own decision - "the Twisties are a savoury snack, the Skittles are sweets. Eating Twisties will make you thirsty and it's already a hot day. Or you could get Twisties if you REALLY want a savoury snack, and I will buy you a piece of fruit in the greengrocer's at our next stop, so you can have something sweet too, but healthy."
Once the trolley is loaded, we get to the checkout. Now some of our checkouts now are lolly-free, which is a good thing. It matters less now, because difficult child 3 is more responsible now. But for some mothers this is a godsend.
So at the checkout, assuming no tantrums, I still keep kids busy. "We have to load the shopping onto the conveyor belt. And we have to think about it as we go - heavy, solid things first, like tins, bottles of drink and juice, bags of cereal, toilet paper; then bread, eggs, crisps. Make sure all cold things are put together - except my carton of milk, I want that now, not when we get home - and then we can pack the trolley more sensibly."
Then we declare "no bags!" to the checkout operator and quickly whip round to the output end and pack the shopping back in the trolley again, following the same rules. Kids LOVE to help and you have to forgive the occasional cracked egg, or tin of soup smashing the crisps to powder.
Then either back to the car to unload, if the trolley is too full, or into the greengrocer first to get the fresh fruit and vegetables. Again, the kids are permitted a treat as long as it is inexpensive. difficult child 3 LOVES a bunch of Dutch carrots (aka baby carrots, still with their green tops on, all tied into one big bunch). He's generally eaten the entire bunch before we get home, then takes the green tops to feed to the chooks (aka hens).
I'm more generous with fruit & veg snacks because they are so healthy. difficult child 3 also loves grapes, apples, red capsicum and tomatoes. He ADORES peas as a special treat.
Something it is important to remember - a lot of difficult children simply can't cope with the noise, bustle and activity of a shopping expedition. Keeping it short, low-stimulus, brief also helps to keep it positive. If you can leave before there are problems, DEFINITELY reward. If he's noisy but happy, ignore the noise. If he will wear earplugs and sunglasses, let him (even inside) because it reduces the sensory input, especially for a kid with Sensory Integration Disorder (SID). But if you can keep the kid occupied positively and constantly praise for each small job done well, you will be on the path to teaching them how to help, rather than seeing them continue to hinder.
Your kids are only 3 and 5. Still very young, even for PCs, to be able to cope with a long shop. Where possible I would shop early in the day, during school hours. If they are in day care and you work, then shop in your lunch break if you can. And if you have to make two shorter trips it is much better than one which is too long for them.
Plan in play times for them - we have play areas in our mall where the kids (especially really little ones) can play in a supervised area while the parent has coffee. You can't leave the kids there, you have to stay, it takes about half an hour,. but it burns off a lot of the frustration energy and especially if you then feed them, it makes a subsequent grocery shop much easier.
If you have even a moderately good shopping excursion, reward them with a special trip to a nearby park or with some game time with you once you get home. Find a way to catch them out being good, and reinforce it. If they're not good, cut short your trip and take them home.
I also, when difficult child 3 was very young, had him labelled. I got a roll of sticky name tag labels in bright colours and before we left the car, I would write on the label his first name and my mobile phone number. I did two labels - one on his front (which he often pulled off) and one on his back. That way if he wandered off or got lost, I could be contacted. I also had a velcro wrist tag label which lived in the car and which he would put on before we went shopping. And when he was very young and a real headache, we had a leash for him. One end went round my wrist, the other went round his, and a coiled plastic cord kept us tethered to each other. That way he could consider that I was on HIS leash.
Shopping with little kids ain't fun. It's harder when they're difficult child. But it sounds like you're doing well, considering.
Don't sweat it. Don't be concerned by the glares - just imagine seeing them trying to cope with your darling, with zero experience and smile to yourself.
Marg