Hey Tom, I am sorry for your loss, and sorry you are going through this.
One thing I have observed when a loved one passes is that people are often not very rational, and material things take on more importance than they should. It feels a little like the last piece of the person and some struggle to hold onto as much of it as they can.
When my mother died she did not have a lot of money, but what she did she gave to us before passing. All that was left were the things in her house. I met with my brothers to talk about dividing things up, and it quickly became emotional and adversarial. So I just grabbed a cooking pot, told them to sort it out, and left. Now looking back those things were trivial, don't know why it felt so important at the time.
Sounds like the house is legally your sister's, should not be a question there. She should resist anyone trying to convince her to give it away. Best to try and let everything else go as best you can. Just remember your father. Sounds like he was considerate with respect to the funeral planning.
Try to eat well, I know it may not seem important now, but it is something you can control, and you'll feel better if you do.