What concerns me about what you have shared is how your finance tends to take her anger and insecurities out on you. Yes, it's such a challenge in that she is worried about her father and if she will pass the tests so she can save his life. That is very understandably extremely challenging and stressful. It was not nice that your mother and sister were mean to her either on top of her having this big challenge about her father. It sounds like she is feeling very frightened as often that is where anger can come from, "fear".

I think that it is wise for you to hold off making any plans about marrying her until she gets through this challenge with her father and you can slowly see if she can find a calm instead of blaming you and taking her anger out on you for how she is feeling so vulnerable. This isn't about cutting and running with her either, instead it's seeing if you can work this out despite how vulnerable she is feeling about suddenly having to do something so important in order to save her father's life.

I have a feeling your gf is still young yet too. Honestly, one cannot expect someone to JUST KNOW how to handle some significant life challenges. This is something we all learn to do as we grow as a person and truth is we actually do this our entire lives.