"Please don't tell me how to parent my kids"
We wouldn't have to, if you actually did parent them, @cookiesandchocolate.
Use straps to secure the 2-year-old into the trolley, and a backpack with reins to keep the 4-year-old with you. Put effective consequences in place for bad behaviour, and enforce them. Keep on doing so, even if the children tantrum. Or run the risk of raising children who have no idea how to behave, how to do as they are told, and find school and life in general much harder than it needed to be - and their struggles will be your fault.
I am not a perfect parent - I know I have not always dealt with the boys' behaviour in the best way - I remember once, when ds1 was having an epic 45 minute tantrum, before 9am, having had an even more epic 90 minute one the day before, and I was on the phone in tears to dh, when it went quiet - and on investigation, I found him at the bin, eating the leftover tortilla chips dh and I had thrown away the night before - and I let him carry on eating them, because I couldn't FACE a third tantrum in less than 12 hours - but I learned how to deal with tantrums, and I did discipline my boys.
They have grown up to be pretty decent human beings - good people to know, hard working, successful, popular and pretty law-abiding. They aren't perfect, nor am I. But I tried, damn hard, to be the best I could be, as a parent, because they deserved nothing less.
@Mummymummums - like you, I worry about my elderly, frail mother's safety in supermarkets, if parents think it is OK for their children to run riot or scoot around. Mum has a degenerative spinal condition which causes her severe pain, and spent 7 weeks in hospital over Christmas and New year, with a bad infection in her knee joint that has severely impacted her mobility and balance - and I dread to think what damage could be done if she were knocked over like @auditqueen's dad.