No one's getting back at him. Joshua wants to make things clear between brothers. And for your information , a psychopath traumatizes you for life and you just leave it cause "he doesn't understand that" is a total bullshit. He committed crime , he must be punished. It's actually bare minimum , that Joshua is not doing anything dangerous. If my boyfriend was violated by someone like Grayson , I'd kill him and sell their organs lol
While I do agree with some of the things you said, I still want to clarify that Joshua's intention is to get back at Grayson. It is clearly said in the novel but he just used the other term to describe it. That's also what Dane is doing right now. It would be nonsense if they just kidnapped him and have a talk? What's the purpose of kidnapping if they can just ask him to have a talk. The talk is part of it but they still plan to beat him but not to extent that they will kill him. Don't make it look like they are angels too
Their personalities are the reason. Chase is a tsundere, who easily blows up.
While Grayson is more calm and talks back. Chase blows up while Grayson only sees his little bother who needs to be cared for. So Chase get's the impression that no one takes him seriously and gets frustrated.
So I guess what Josh wants to do is gag Grayson so he can't talk back und let Chase talk everything of his chest without being disrupted or getting riled up.
But as the OP says, it's a waste of time. What Chase wants is a sincere apology, means that Grayson understands him, which was actually one of Chase's bigest problem with the family -communication problems where no one really understood him. That's something he won't get from Grayson, unless Grayson starts to understands emotions.

Honestly they are all pissing me off.
Yeah what Grayson did to his brother was cruel, but that guy does not understand this. He does not understand normal human relationships or feeling. Them trying to get back at him is simply stupid