Update:
So I just had the chance to talk on Sunday with my sister-in-law's husband. He came to visit all of my wife's siblings and their spouses, and it was the first time any of us had seen him since the separation. If there is any silver lining in this hard situation, he has turned toward God completely and has been asking to do His will. He is seeing a Christian counselor, attending church regularly, and praying earnestly. He has spent more quality time with his daughters than he ever had, he is trying to show a love for his wife that he never realized he had been neglecting, and overall, he is trying to both win her back, and be the leader of his family that God called him to be. He was very open and honest with all of us, he admitted his mistakes, and he has apologized to his wife and the whole family for the way things were. He is also working again, for better pay and with a more reasonable schedule (part of the reason the marriage struggled was the taxing job schedule he maintained) and he is generally in as good of a place as he can be given his situation.
My wife's sister on the other hand, has not been doing as well. She doesn't seem to know what she wants, and she thinks the only way she'll be "happy" is with a divorce and seems determined that that will be the outcome. They do still talk regularly (as they have joint custody of the girls) and according to him, she doesn't feel like he's being sincere. She will give him hope for a day that things might work out and the next day seem adamant that she wants out. She also seems to want a divorce to go "smoothly", and that they will both agree it is best for them and the girls. Very wisely I believe, he refuses to support the divorce, refuses to tell his daughters that it's going to be okay and it will be for the best, and he refuses to have any part of the divorce except for signing the papers if she forces his hand.
So prayer for three things:
First, that he would be encouraged to stay strong on the positive path he has been on these past few months. He refuses to say anything disrespectful or hurtful to his wife or the family, and he is continuously encouraging his daughters to love their mother and trust God.
Second, that God would heal her heart to see that He loves her, and that her husband loves her too, and wants to do whatever it takes to repair the relationship. She needs to feel love from her husband that she hasn't felt strongly in years, and she needs to feel love for her husband that she can't seem to muster up right now.
Third, that we as their family would not "pick sides" or pressure them to do what we think is best. One of the hardest parts of Sunday's meeting was afterwards, when my wife looked very somber. We left, and I asked her what she was thinking. She basically said that now that she heard his side of the story (all she had heard before was from her sister) she feels differently than she did about the whole thing. It would be natural I guess for my wife to support her sister offhand, but from a Biblical standpoint, we can't support the stance her sister has taken, now that we have seen his heart. We know that divorce will not make anyone truly happier, and now that we have seen the changes that have taken place in his life, we are confident that the marriage should survive. But we also know that God needs to do some serious work for her before that can be settled, and she needs to let Him work, which can take time.
Thanks for reading, and please continue to pray.