You're the only one who can decide what's OK for your life and what isn't. If your SIL has been the go-between for 20 years, then by all means let her continue to be it. Apparently that's worked for 20 years, so why would YOU need to get involved in what has become her family "job". If she feels taken advantage of, she's either a door mat having put up with this for 20 years or she's satisfied with her place in the family.
If you try to get involved with her responsibilities to make your husband happy, you're only asking for dissatisfaction among the family members who have chosen to set her up as the family organizer. I wouldn't go out of my way to try to insert yourself into there already-set situation which seems to be working.
If somebody calls you and says "Dad is having a party on Saturday are you coming?" then tell them "yes" or "no"...but don't volunteer to call the rest of the family members to invite them and find out if they are going to attend. If you're asked to spread the news, you can say you'll tell the people you run into, but that you'll leave it to SIL to be the "official" family calendar.
If you call messed-up SIL to discuss the loss of her job, tell her you're sorry she wasn't able to keep the job and ask her what she plans to do about it. Listen a couple minutes, then walk to your front door and ring the doorbell and say "OH somebody's at the door...gotta go!" and hang up. You won't have to sympathize with her and you won't have to tell her you think she's scum. Then, you can tell your husband honestly that you called her...IF you decide that's what you want to do.
No, you don't have to play games with his family if you don't want to. Play it simply by doing the minimum and don't make it a huge deal with your hubby and let it become an issue for hubby and you by constantly arguing about it.