You can school him by giving a little bit of a chase... not too much because it escalates things. Teen age hormones are the worst.
I personally would NOT have any rooster with a 2 and 3 year old. In case containment fails (or if free range) they could be blinded by a flogging and be traumatized against chickens. I've been spurred before... it really hurts, left good size bruises and some puncture wounds. Kids are smaller, easier targets.
I would rehome him or give him a nice long hot bath with some aromatic veggies.
Cockerel is not a good choice for a first chicken with kids. I hope you are able to reconsider... raising your chicks and maybe adding a rooster next year if you still want one.
He is young... he MAY reform still. Like many teens he WILL test his boundaries... and he see's you as NOT intimidating. I wanted my first boy to trust me... thought that's what was going on until I faced constant stalking from behind the fence, attacks from behind, and relentless crowing directly AT me. I took it for a while since it was a "rare breed" intended for breeding, trying all the training techniques. It was too late for THAT boy.

After several months, I finally got fed up and sent him to freezer camp. It took several months after that for me to settle down and not take other boys crowing personal. Almost ruined roosters for me permanently due to my inexperience.

Thankfully I did recover... I have a constant barrage of cockerels/roosters since I hatch. I have NEVER yet again faced that with any of my boys... I don't be over friendly with them. I just treat them like chickens... who now I know FEAR = RESPECT for shooks. You start to notice the clues they give off earlier. Never ever let them get away with dropping a wing and dancing at you. And he will mate your pullets before they are ready since he is still young and dumb. All my stags get to grow out long enough to gain their manners before mingling with the ladies.
A good rooster is a great asset!
That is great reading from BEE... it isn't my style and didn't work for
me... but being clued in HELPS a LOT.
Also, if your kids will have others over to play... might not be worth the liability.
Also note... yes I will accept and deal with a single challenge or two. Agree kicking escalates attack... chucka gave good advice.
Best wishes!