@John D. RodburnWait, hang on, you can't possibly be describing this correctly because I have no idea how you think this supports "hitting kids helps them learn".
Let me summarize and maybe you can point out where I'm getting it wrong.
You have two boys, Joe (older) and Tim (younger). Joe has a fascination with touching Tim's eyes, you told him not to, and eventually you found the "final solution", as you term it, and when Joe went to touch Tim's eyes you hit him pretty hard. When Joe went to touch Tim's eye, you would prepare to hit him again, and Joe would stop.
Anyways, Joe touched Tim's eye again, scratched it pretty bad, and so you hit him a lot more, and told him not to touch Tim's eye, and there were no repeat incidents.
So uh, I'm not sure why you call hitting Joe on the hand the final solution, because it wasn't at all? Your story here is "my two year old had poor impulse control and so I hit him, which weirdly failed to solve his poor impulse control and so I had to go really beat up my two year old, who statistically had a vocabulary of somewhere between two to three hundred words and had recently mastered the art of combining two words together into a coherent phrase, and this didn't fully solve the problem but I was able to intervene every time it came up again".
Like holy fuck dude. You left your two year old unsupervised with your newborn infant, and bad things happened, that's why you probably shouldn't leave your two year old unsupervised in an area that is not child-proof? A space with a newborn is not child-proofed for a toddler, because part of child proofing a space is making sure that there's nothing they can damage or hurt themselves with in the area to avoid exactly scenarios like what you describe. So uh, my answer to how I prevent the first scenario is "the scenario is the result of parental malfeasance, so I would simply not leave my toddler in a situation where they had the unsupervised opportunity to touch my newborn's eyes, especially after they had repeatedly expressed an interest in touching the eyes."
I have one child, a little under 18 months old; I also have two cats. One cat generally fucks off and stays out of reach, the other is extremely social and has always loved to hang out with the baby. Since literally day one introductions we have stressed "gentle hands with kitty, no hitting, no grabbing, gentle hands" and demonstrate slow open hand petting the kitty, even holding my child's hand and moving it across the cat so he can feel what it's like. He is, at this point, pretty good at gentle hands. We still don't leave him unsupervised with the cat and if he's petting the cat one of us is always keeping a very close eye on him because sometimes it's hard and he forgets, because he's ~18 months old. Your kid had barely started moving past peekaboo being the height of entertainment and you decided it was easier to really beat him up than to make a place in your house where he could safely entertain himself, Jesus. I feel so sorry for Joe here.
Okay, situation two, which I'll sum up again. Tim is acting out (and probably with some mild anger issues, if you've treated him at all like you did his older brother) and reacting poorly to the arrival of a newborn. You leave both your eight year old and your six year old unsupervised regularly with your two year old - you neatly sidestep this issue by saying "only a moron would say to never leave their children unattended" which i'm gonna have to disagree there, dude, you should absolutely not be leaving your two year old unattended and you should absolutely not be making your eight year old responsible for supervising both his younger brother and his toddler brother?
Anyways, so Tim is acting up. He's got parents who leave him alone and unsupervised and he's got a dad who would rather hit first and then hit second as well because hitting first didn't solve the problem, but he didn't choose his family so he's kinda stuck with the situation. Poor Tim.
The specific way in which Tim is acting up is by tormenting his two year old brother, an outcome that's completely unforeseeable until you read literally any parenting book about raising multiple children and get to the chapter that talks about how older kids can often resent younger siblings for taking parental attention away and act out as a way to force getting attention, because getting negative attention is better than being ignored. So one question that's top of mind here is "does Tim feel like he is getting quality time with his parents, both of them together and also special one-on-one time with mom and with dad?" Considering that Dad has habitually been leaving Tim unattended since birth, and believes that only a moron would never leave a two year old unsupervised, I feel like we can infer a pretty solid answer here. You start hitting tim, which takes a while to really sink in, and the behavior fades.
I would handle that issue by a) not leaving my two year old child alone and supervised exclusively by other children. That's why people pay for daycare or a nanny or leave their kids with family while they're at work. Yes, it's expensive, kids are expensive. The one weird trick you've discovered to avoid this expense is parental neglect.
Anyways, I would also b) make sure that I set aside specific and regular one-on-one time with both of my older children to talk to them and make sure they are getting actual attention from me, which means that now they don't need to act out to get attention. Will this solve the problem instantly? No, probably not, but also neither did winding up and really letting loose on your kid's ass, and on the whole, spending positive time with your kid sounds a lot more fair than posting a sign that says "the beatings will continue until morale improves" and pointing to it meaningfully every morning when you leave your kids alone and go work upstairs.
Edit: I also want to briefly address this part about tantrums, now that I've finished processing the story about how you ignore your kids and then hit them when they get into trouble that you should have seen coming if you weren't ignoring your kids.
Children will test you and see what they can get away with. If there is no strong enough deterrent, they will keep pushing and will find the best ways to extort you. Tantrums are their way to disrupt you until you give them something you don't want to give.
β¦so? A couple days ago my toddler had a tantrum. We were cooking burgers on the grill. He wanted to be involved, a developmentally appropriate milestone for his age, and we would not let him touch the grill. This was upsetting, and so he started screaming and crying, inconsolable.
We said "I can hear that you're upset, bud! You want to help and you can't, and that's pretty tough. But you can't touch the grill because it's not safe, and I love you too much to let you do that." And continued cooking the burgers. When I had a chance, I made an effort to redirect him into playing with trucks and that worked for a bit, then he wanted to help mom again, melted down again, and we just let it happen. Sometimes toddlers are upset and they have tantrums, you don't have to respond. You can just say "that's rough, kiddo" and let them be upset and if they are open to being redirected you can redirect them and if what they want to do is be upset, you can just let them explore those emotions in a safe, controlled environment where you are supervising them and making sure they don't hurt themselves or somebody around them.
If you're not a parent, you can say that I should always be present, or their mom should be present, but that's not always possible and only a moron would suggest that.
Depending on the eight year old, I can see case-by-case arguments for leaving them home alone. Every child matures at a different rate, so I don't want to lay down a blanket pronouncement about when a kid is old enough to manage themselves for short periods of time - at eight, I think you can probably talk with them to go through things like "I'll be out of the house for two hours, if there's an emergency, what do you do?" Etc and get a sense for if the child feels confident about the situation. Depending on the two children, I can even maybe see leaving them alone together if the six year old is on the mature side. If there's a two year old in the mix, that changes things dramatically. You should not be leaving a two year old unsupervised and an eight year old does not count as supervision. How do we know this is a bad plan? Maybe your eight year old tells you, in tears, that things go wrong and he isn't able to fix the situation? That seems like a pretty solid indication that your plan of "have my third grader be a single parent of two for the day, five days a week" is a bad one. You're the adult, you had three kids, it is your responsibility to line up care for them. That's hard! Nobody said being a parent was easy, that's why we try to warn teenagers off it! I'll readily agree that hitting your kids is way easier than being a parent, but that doesn't make it a good option.