I read this thread when you posted it, WatchingMyChicken, and came back to re-read it, and what strikes me is how abusive the dynamic feels.
The sibling is effectively using your DH to vomit all their undigested, unprocessed trauma into on a regular basis, and your DH is left incapacitated by this input of toxic waste for days afterwards - but still keeps going back and allowing the sibling to do the same over and over again.
It works for the sibling. They can function, they have a life, job, partner, family, and because your DH is playing the role of emotional waste bucket, they can and could continue in this cycle indefinitely. It’s very telling, as others have said, that they are so protective over their own boundaries and family time, to the point of missing your DH’s milestone birthday, but your DH is unable to be even remotely protective of his family time, or set any boundaries at all.
It doesn’t, on the surface, work for your DH. It’s almost like a master/slave dynamic. The sibling demands everything and gives nothing, your DH gives everything and demands nothing.
And yet they are both adults, who were both impacted by this trauma. Why is it only the sibling who is allowed to be selfish (who sounds actually quite narcissistic tbh), to need support, to have their needs met in this relationship while giving nothing in return? While actually making your DH’s life harder and more painful? Some people have said what if the sibling became suicidal if your DH didn’t run to enable; well, what if your DH became suicidal as a result of this ongoing stress and repeated stirring up of his own trauma? Would the sibling take responsibility for that?
Why is there an unspoken agreement that one adult (your DH) is responsible for the well-being of another adult (his sibling) but there is no reciprocity at all?
Your DH sounds hugely co-dependent. He has no boundaries, no understanding that we are all entitled to be selfish to a degree, that it is actually unhealthy to never put your own needs first. But he must be getting something out of this. Perhaps some kind of validation that he is a “good” person. That he is powerful enough to make his sibling better. Maybe he has avoided really processing the trauma himself, and “being there” for his sibling actually serves a purpose for him on some unconscious level; maybe it’s guilt that makes him keep going through this; there could be a myriad of reasons - but just as the sibling needs to want to change this situation for anything in their life to shift, your DH also needs to want his dynamic with the sibling to change in order for anything different to happen.
The sibling isn’t going to be open to suggestions for what to do differently because the current situation is working for them. Neither is your DH going to do anything to rock the boat because as long as you are there to pick up the slack, be his emotional buffer, keep his home/emotional life running, and take care of his child, it’s working for him too, crappy though it may be. It’s bad, but it’s not unacceptable.
This will carry on until someone says it’s unacceptable. It looks like the only person who might do that is you. You’ve taken the first step - good for you. You have every right to say this is intolerable and while it may be true that stopping enabling the sibling would be good for them too, you don’t have to approach it from that angle. You are entitled to put your needs first yourself, and to ask your DH to prioritise you and your child.
In fact, as parents, you should both be prioritising your child above everybody else. The sibling has agency and choices in this situation that your child simply doesn’t have. And your child will undoubtedly be affected by this in years to come if the situation doesn’t change. Please don’t understate (to yourself) how unhealthy this is, how much things need to change. You have a right to a decent quality of life, not this protracted struggle that you only just make it through, and a decent quality for life is all you're asking for. Your DH’s sibling has that same right too of course, but it is up to them to achieve that in a way that doesn’t require you and your DH to sacrifice your own happiness.
Very definitely, YANBU.