Op You are doing a great job! My son is three and a nightmare in public spaces. I am not a lax parent I have tone in my voice, clear instruction, boundaries.... but he still runs riot!
Every person on here has had the experience you have described with their young children, they either have forgotten or decided that being a keyboard warrior is far more entertaining.
I know it's hard when strangers judge, but remember they don't know you, your parenting and they are judging a micro moment in your child's life - says more about them than you!
Ignore the reins and trolley seats brigade too- these solutions are not always solutions to certain children. My child won't sit down in a trolley seat, and will collapse into a volcanic eruption if I dare put reins on him. Trying to rationalise with the unrational is like platting fog!
3 is such a tough time, you are surviving, they are thriving, it's absolutely normal behaviour... some tantrum battles you win, others you don't. But it's absolutely no reflection on you, it's just that dreaded developmental stage!
You are being a great mom.
Oh last thing a couple of weeks ago my son had a complete meltdown in a shoe shop, he absolutely wouldn't try on shoes, screaming so loudly bats could hear, he was a snot volcano. I decided to pack up our things and save the good people's ear drums but of course he grew a spine and wouldn't sit in his push chair. Kindly a man sat next to him and started pulling faces, the shop assistant brought him tissues, someone else started saying to him at his level how lovely his smile was. The kindness of strangers was unreal! We managed to get his feet measured in the pram and out with smiles.
Not every stranger judges, so don't be defeated! X