I haven't read through all the pages here, but I saw enough to understand that that there are common themes that I wanted to comment on. 1) the OP said that it was a 'sad' observation. And I have to agree that it is sad that a Mom trying to provide an enjoyable enriching experience for her kids on her own (at least on that day) can't get any help from her boys. I don't think this translates to 'bad' parenting nor those kids will grow up to be 'good for nothings'.
I was raised more traditionally where kids listened to their elders (all of them), didn't talk back, showed respect, did what they were told when they were told, etc. I struggle with the same issues where my kids simply will not do most things without being told 3 times--at home, in public, where ever...(Note that all of my kids are excellent in school in both grades & behaviour so they do understand on some level what is acceptable.)
Yes, I am that Mom yelling at her kids because it drives me crazy! Regarding the Mom in the post, she was likely distracted by the fact that she was loading the car and didn't notice that they had done nothing until she was done packing the car. I know this happens to me--I tell my kids to clean their room.They go to their room and I go to cook dinner and see them watching television 15 minutes later. We eat, watch TV, read, play games, and I send them to bathe and go to bed. I go in to say good night and their room is a MESS! Now it's bed time on a school night and I have to make them get out of bed to clean up (after going nutso as PP said).
2) And yes, that Mom will likely be at the beach or whereever next weekend despite her 'disappointment'. I've been there, done that too. On this point all I can say is that, for me at least, 100% compliance is not as important than spending quality time with my family. Taking away toys, games, tv, are fair game (but so far have not proven effective--but my kids are still young, hoping that the currency of phone & internet will become stronger as they age

)
Times are different. Parenting is difficult. Kids are individuals.
There is no perfect formula and many of us are doing the best that we can. In my day, that meant that I didn't have a voice as a child, had to live within very strict guidelines , and was sometimes spanked. I learned many valuable lessons that make me the person I am today, but there were somethings, frankly that I could've done without. So as a Mom, I try to find the balance, focus on the things that are important to me--education, honesty, kindness, self-worth, creativity & independent thinking. And for all the other stuff, well there is the occasional Mommy freakout. for that.