Well, this is a lot to unpack. Since telling you what to say is impossible given that we don't know anyone, the suggestion would be to ensure first that you are taking care of your wife. As someone with a mother who barely talks to me, and pretty strained relationships with extended family for similar reasons, I can tell you that the people in my house, my husband and my daughter, are the ones that make the most difference in my day. My husband constantly tries to ensureassure me that my mother's behavior is not normal, we spend a lot of time with his parents, who are wonderful, and when my mom calls - which is rare - iI go ahead and get through it knowing that whatever she says, I still have my people around me who care, as your wife clearly does, too. There will likely be many ways you can help - this is just one person's suggestion:
Continue to show the care and support you clearly have so far. Knowing she has you does make a difference.
Consider her seeing a therapist or going together, so she can get the feelings out (and have you there to support her if you go together). Therapists are trained to deal with depression and also may have good strategies after understanding the dynamic better.
Reassure her that just because they call or email doesn't mean she has to answer every single time.
From the sounds of it, there is no real surprise that her sister has left the family. The behavior sounds toxic and if I read between the lines it seems that there is more to the story with your in-laws, whether it is an inability to communicate, or perhaps depression (which can be hereditary) that is untreated.
I'm not suggesting that you not speak with your in-laws, but ensuring your wife is safe and working on making herself happy without them has the potential to work best for her in the long run. A person can control their own feelings and how they are affected by others much better than they can control other people.
Making your own fun plans, booking your own fun trips, and limiting exposure to toxic people while you work this out might be one way to handle it.