DH was going to leave because he admitted he was the cause of all the problems in the house
Sorry, but that's bullshit. No one can ever be the cause of ALL the problems in the house, and it's not fair to say that our let him take that on himself.
You've already said that you're too soft on DD. That's a problem.
You've said DD is manipulative. That's a problem.
He might have been ott. He might have been a pita.
He might even have been abusive.
But he can't have been the only problem in the house, and if you really think that, then you need to do some serious thinking. And possibly some self- examination.
And the incident you described didn't sound the slightest bit ott. And in that situation, it sounds like he was the only one behaving reasonably.
It's funny that in the op, to were annoyed with his handling of the situation. Now suddenly he's an abuser, and you're just waiting for a relapse. And he is trying really hard, (apparently the only one in the house!) But all the blame lies at his feet.
Ok then.