I would not hate you
or feel sorry for you. I would avoid you though! I wouldn't think you were a bad mum at all but I would think you were probably overwhelmed.
I have no patience for badly behaved children over toddler age, but especially not in public. I would consider wrestling and picking things up repeatedly badly behaved. But then I have a long list of things I consider unacceptable so I'm probably too strict!
I don't judge other people by my standards and would never say a word unless asked. I think it is a shame for the kids though. Other people would judge them and it's not their fault.
Children have little willpower and when people describe their badly behaved children as being strong-willed, in fact, the opposite is true. They are weak-willed and need to learn the art of self-control and delayed gratification.
I have the attitude that my children should only inconvenience me or their Dad. So if ours did this, we would leave. It would be hugely inconvenient but I have been known to leave a meal unfinished, and a trolley in an aisle over the years. I know lots of people disagree with this though.
I would think you are making life very hard for yourself in the future by not setting very clear boundaries now. I don't agree with the idea that well behaved children are down to luck. Most times I see a badly behaved child they are usually accompanied by an ineffective parent, endlessly repeating their name.
I know I will be accused of being smug but mine would never, ever do this. Over the age of about 3 their behaviour was reliable enough to not have to worry about it. I may have just been very lucky and given birth to 5 exceptionally compliant children though!
I think when you have multiple children there is more pressure to ensure they are well behaved. One badly behaved child could be bad luck or down to a lack of parenting experience. 2 is very unlucky. More than 3 badly behaved kids running riot is definitely down to parenting!
When my youngest was a newborn my others were 3, 5, 8 and 11. I know it is hard work but if you don't find a way of getting them to comply now then it is only going to get harder as they get older.
I'm sure that you are a lovely mum and that your kids are lovely too. My comments are only in relation to what you have shared. I would smile sympathetically if I saw you and would never want to make someone feel bad. We all have bad days.