OK, I'm blaming this on public school and TV.
Well who sends them to public school and who allows them to watch TV?
As the father of four toddler boys (triplet 2 yr olds and a three year old) I can attest to their ability to get into things on occasion, but nothing like the cousins in this story. My boys do not watch TV, have plenty of outdoor time on our playground, and have already begun a healthy prayer life. When they are destructive it usually involves their own toys. They did break a few rosaries when they were first learning to use them and they often rip books by accident, but over all they have good self-control.
The thing that keeps them out of real trouble is their mom. ( for my DW) She knows them well enough to sense when one or more may be about to get out of hand. She also recognizes their innate need to have something interesting to do and, on occasion, something ‘destructive’ to do. One of our boys, Gabriel, loves to pick flowers. DW has cheep mums that he can pick. This week all of them are into destroying leaf piles. The ground rules on certain things have been set from infancy: no grabing food from the fridge or pantry, be creative with paper, not walls, leave electronics and medicine to the adults.
So I would say that the most important aspect of keeping toddlers out of trouble is good parenting. At the age of two I wouldn’t think we can generalize about homeschooling v. private or public schooling. Perhaps the effect of having older siblings who are in school v. having older siblings who are homeschooled could be a link to behavior. My oldest is nine and attends a Catholic school. So far no problem. Her younger siblings look up to her and take their cue from her respect for us.
One more thing, regular prayers to their guardian angels help a great deal. I could tell some great stories about what DW and I percieve to be help from their guardians.