..... is [this] something that a rooster coming into his “manhood” does?
Yes, pretty much. Most do, some don't. Their teenage hormones will settle down after about one year of age or after their first molt. But some will always be aggressive. You won't know until he's older. BTW, a male chicken is a "cockerel" until he's one year old, and then he's a rooster. Female chickens are "pullets" until about the same age, and then they are hens.
Like is my other rooster going to start doing the same thing once this is gone?
Maybe, maybe not. But some cockerels/roosters are more aggressive with the hens than others. You'll just have to take your chances, and see what he does and how the hens react. I agree that the aggressive one needs to go, or at least be separated from the group until he comes into full maturity and settles down.
If they haven't already started fighting each other, it's likely they will - unless your 2nd cockerel is agreeable to take last place and live as a bachelor his whole life. But that's rare.
How do you know if you’ve got a good rooster I guess is what I’m really trying to figure out…
It's hard to identify a "good" cockerel until he's over one year of age, but some will start practicing these behaviors as early as 16-18 weeks. As he grows, observe him carefully for these behaviors:
If you keep a backyard flock and wish to interact with them and enjoy spending time with them, and especially if you expect to have children around: The most important trait is a rooster who *never* challenges humans, but always turns away when you approach. Try walking 'through' him and see what he does. He should get out of your way with no question, every single time.
Other requirements for a "good" rooster (whether or not you wish him to behave with humans): One who defends the flock against any threat, even to the death; constantly observant of the surroundings; calls alarm when he sees a threat; alerts the hens to food he's found or to good nesting spots; breaks up fights between the hens and disciplines troublemakers; herds the flock towards the coop at roosting time and often is the last to enter; and is gentle with the ladies (although grabbing their neck feathers in his beak is necessary to mate, he shouldn't pull out feathers or draw blood). If he's good with all of the above, and the hens are sexually mature and ready to mate, you'll see the ladies readily crouch for him when he dances (they've decided he's a keeper).
As long as both boys are together, any aggressive behavior in one is likely influenced by the presence of the other. If you have the equipment and space, you could separate them from the flock AND from each other, but still where the hens can see and talk to them; and then re-introduce one or the other to the flock for a few weeks and see what happens.
Still, you won't know for sure until they're older. It's really just a crap shoot; you can't train them to be good. They either are, or they aren't.
