Parenting small children

I have one and three year old sons, and they fight over toys and scream and hit each other, and although on some level I accept that this is all typical toddler behavior, I often make it mean that I am a terrible mother and that if I don’t figure this parenting thing out soon, they will become bullies. I know we cannot control others, but isn’t the point of parenting to somehow manipulate our children into behaving the way we want them to through rewards and punishments? If I just work on my own thoughts, won’t I be doing them a disservice by sitting calmly while they run amok? On the other hand, the parenting techniques I’ve tried with counting and time outs and other consequences don’t seem to make much difference either.

C: I have kids
T: My kids are misbehaving which means I’m a bad mom
F: frustration
A: yelling/punishment
R: my kids cry and I feel like an even worse mom

C: I have kids
T: kids will be kids
F: calm
A: ignore misbehavior, inaction
R: misbehavior persists

There has to be a way to use the model parenting toddlers!