Family dynamics can be intergenerational. When a child grows up in a family with dysfunction- it's the "normal" they know. They, then may repeat these patterns as an adult. While you may see the dysfunction in your H's family- they may have grown up in this too- and don't see it themselves. Other family members might not have BPD themselves but have learned behaviors. It's also not only in families where someone has BPD. Changing this pattern may require someone going to therapy and learning new behaviors if they are able to do that.
One common pattern is Karpman triangle dynamics.
https://www.bpdfamily.com/content/karpman-drama-triangleAnother is where there's a person with a disorder, or addiction, and other family members are enablers. People who are enabling the person assume they are helping them but they may also be enabling the person's disorder.
I think you are correct about not wanting to rock the boat in this close family as you would be seen as the one being disruptive. My BPD mother's family would rally to her side rather than to consider other possibilities.
We can't change another person, and this also extends to other family members too. It's understandable that you are concerned this situation may interfere with your H's working on himself. For someone to do this work, they, themselves, need to be motivated to do it. So, family or not, this is his work to do. So while his family may be an issue in him doing this- your H is the one who is responsible for his own therapy. There are two sides to this- while it may appear his family is ruining the last shot- he also is a part of this- they aren't to blame entirely. Just like he's a part of the situation- so are they and they will continue to be his family. I hope for all of you that he does the work but it will ultimately be up to him.