I was able to train a rooster to not attack me. I was not able to train him to not attack my wife or other people. If your kids were old enough they could probably train him to not attack them. I don't think they are. And what if your kids had visitors over?
I understand the desire to hatch your own eggs. You can always try another rooster, many do work out. But if you get a broody hen why not just get hatching eggs form that farmer? There is more than one way to solve a problem.
would you say that my responses to him are what caused the aggression?
Impossible to know. Each one is different. Like Mary I believe part of that is heredity, part environment. How much of which can vary from one rooster to another. Some just seem to hatch that way. Some are fine until some event kicks hem over to the dark side.
You say he attacked your three year old first. That kid may have done something to set him off. Maybe not. In either case he is not a threat to her. To me the why doesn't matter, that he is a threat does.
Don't beat yourself up, it's not your fault. If you try it again I'm sure you'll watch the little kids closer. This kind of thing can happen whether you raise the rooster with the flock or bring one in. You always need to be aware. And I've found that breed does not matter.