I have been in a similar situation to your DH, the only difference being the DSC in question moved out just in time to save my relationship with DP and the other DSC.
Please try and understand the place your DH is in just now. Living with step teenagers is hard, and especially hard if you've never built a paternal link with them. And nobody's to blame for that.
Your DH is showing signs of the same sort of anxiety I had, the very thought of being in the same house as what I perceived to be the cause of the problems - eldest DSC - would cause a stress response in me, sometimes days in advance. That manifested itself in mood, attitude and defensive behaviour like trying to keep out of the way. What you see as picking up on the children's behaviour,manners, lack of contribution are all that. It's just impossible to bottle up when you're in 'That Place'.
You feel totally alienated by the family you're trying to be part of. And very much alone. And you blame the DSC for that.
I too went to counselling and at first I focussed on what I wanted to hear from the counsellor - that it was reasonable to expect certain standard of behaviour from the kids, that they should contribute and that as an adult I had a position in the family that should be respected and they needed to change, I was doing the right thing.
But then, and I don't know when or how the conversation moved on but we got to discussing this anxiety issue and that took the lid off the box. A lot of stuff in there but basically it's about your own perception of what is happening and how you CHOOSE to respond to it. And it is a choice.
It's very easy, especially once you start to feel you have a difficult relationship with someone to react on that basis. They're being difficult, so being difficult in return is just what they deserve. But you are feeding the monster in doing that.
Your DH needs to realise that all of these stressful things that are happening are not aimed at him, they aren't a threat, they are just happening. Controlling that flight or fight response to the perceived threat is the answer.
Don't get angry, turn thinking about what just happened and why did it happen to me to simply why did it happen. And then to how a different outcome might be achieved.
There's a lot more carrot than stick with teenagers and step children, combine the two and you're working in the UN at times as a SP. DH needs to know it's not a fight about one of them getting what they want,it's about an outcome both of them accept.
And yes, there is also some relationship rebuilding to be done here. When you go for coffee do you tell DH about it when you get home, is he interested? Maybe next time he can come with you and be part of the conversation in the first place? Go with a suggestion of something DH and DS could do together next time DS is home? As simple as suggesting driving him to the skate park, maybe DH could watch for a bit before leaving DS some space and then talk about ds's skating on the way home.
Just positive interactions.
I'm going through the next round with second DSC and it's no different, exactly the same situations and behaviour and I can sometimes feel the same frustration of a seemingly pointless existence. But knowing you can deal with it if you CHOOSE to is a lot easier.
And if you think your DH is starting to regret from family life, talk to him about it! Pull him back from the brink. Let him know you appreciate him making the effort and you will support him but he needs to keep doing it. In return you will work with DS to do the same.