C.Ann, I am sorry for your loss. Try and stay strong for your sister...she will need you and it doesn't sound as if oyur brothers are going to contribute a lot. Does your sister have children???
As for the practical aspects:
1. Call the funeral home
2. Decide what you BIL will wear if he is laid out. Bring that with you when you go to the funeral home.
3. Try and bring a recent picture of your BIL so that the folks at the funeral home who prepare him will know what he looked like.
4. Get a lot of copies of the death certificate, as others have suggested.
5. Get friendly with one person in the town's probate office, and use that same person as your resource throughout this time. If you speak with multiple people in the probate office each time you call with a question, the waters will get very muddied.
6. Try to find life insurance policies, military records, etc.
7. Pick pallbearers
8. Pick readings for the funeral service(usually your clergyperson has abook with suggested readings that are appropriate)
9. If you want a program of some sort for the funeral service, have someone work on that(if you have a friend or relative that's computer-savvy, this is a good job for them). When each of my ILs died, we had a program listing the pallbearers, the readings, the songs, and a little poem. It was nice. Some people also include a history of the person's life.
10. Write the obituary
11. Determine if you are going to have an after-funeral luncheon or get-together of some sort, and whether it will be at your sister's home or at a restaurant. A small hint based upon personal experience...this is an exhausting time, so if you can see your way clear financially to do it at a restaurant, it makes life MUCH easier. If a restaurant is too expensive, perhaps a catered thing at your sister's house would be more "do-able".
12. Make sure you have plenty of dispoable plates, napkins, silverware etc at your sister's house. People will be stopping by, and bringing foood,drink, desserts etc., or they will be stopping by to pay their respects and it's nice to be able to offer them something. Plus, for you guys, it will be nice to be able to just eat and throw the stuff away rather than worrying about washing dishes etc.
Again, my sympathies on this shocking loss. I will keep you and your family in my prayers.
13. Call your sister's doctor and apprise him/her of the situation, as another poster suggested. You don't want your sister drugged during this time, but a little something to take thee "edge" off might be helpful, especially since she has health issues of her own.
14. Take care of yourself and rest as much as you can. As anothe rposter suggested, call on friends who offer to help and give them specific jobs. People do want to help during times like this, and if you give them something specific to do, they feel better.
15. Consider having someone stay at your sister's house during the wake and funeral period. It's unfortunate, but often houses get robbed during this time because burglars watch the papers and see who died, because they kno that the inhabitatns of the house will be away for an extended period during the wake and the funeral. Also, if you are having people back to your sister's house after the funeral, the person wo stays there can start the coffee, get the table set-up, greet the caterer etc.