Were you ever the screaming kid, or the parent OR both?
No. I counted my blessings with my kids. Since they were around 3 years old, I took 4 kids, aged 3 (triplets) and 1.5 to any store without an incident. This is partly because I told them that if they ever acted up in a store (begging, tantrums, screaming, arguing), we would leave immediately, even if our cart was full. I meant it.
One time we ran errands and it took 7 hours, and no problems. We made three stops that really interested them: Lunch, snack, and Toys R Us. They got to pick one toy out of the $1/$2 aisle as a reward.
I took them to the grocery store, no problems there either. Each trip, I picked out something they could choose for the family. These were usually cereal, snacks, candy, and sometimes they could each choose one thing without a category being specified.They took these choices really seriously, so it felt like they were taking forever to decide. People always asked me, "Are they all yours"?
Same rule for restaurants. We could take them anywhere, and they behaved. The special treat was the restaurant. The managers and other patrons would stop by our table to compliment them. These were some of the same people who would look horrified when we came in -- I got a kick out of that.
They ordered their own food in restaurants, and paid for their personal purchases in stores. When the kids were 8 and 9, we ate lunch at the beach with family friends. The mom got up to pay for her kids (aged 12 and 9), and I asked her where she was going. To pay for what her kids bought. I said sit down, my kids will show them what to do.
At home, of course, they were not always angels.