It's interesting that around the deadline he decided to disclose a secret from Sis about what her grudge is about. He is offering to include you in their R more?
This is a tough situation. YOur sis has created a triangle. Can you end run around H and make the first move with sis and DB her to be the bigger person and put an end to this madness? It would take the wind out of their IMing. Also, I can see how that is the LAST thing you want to do at this time or have the energy for. To have two people being babies and treating you inconsiderately.
If you viewed it as an act of charity to an emotionally stunted sis (and pot stirrer, no doubt), could you do this over time? If so, you would all be on IM together. I doubt your H is talking bad about you on IM to sis. SHe's probably just moaning and groaning about whatever she moans and groans about every day.
I wouldn't like it either if I were you. I'm just trying to think in what way you and H could stay happy without it being a dealbreaker. I continue to think the whole thing would be less fun for sis if she knew you didn't care and were over it. She might take less interest in IM with H too. If she's really a troublemaker though, I can see how you would not want to deal with her drama every week.
I can only suggest ODP on this for two weeks so you can get more opinions on here and have time to think about it. Do not blow things up with H over this at this time. Try to figure out a new way to handle this that does not make you feel like a doormat.
I'm sorry you are going through this. It is a tough one given all you have already endured and put up with this year. You deserve an award or a new harness for Madam or something!
