I am very sorry for your loss.
I can't even begin to imagine what it must be like to suddenly lose your mother...
I'm a medical student and can try to answer whatever questions you may have. With only your description of the symptoms of intense abdominal pain with radiation to the back, nausea and vomiting, the main condition that comes to mind is acute pancreatitis, which is inflammation of the pancreas that often leads to death. The main causes of pancreatitis are alcohol (usually only in alcoholics), gallstones obstructing a duct, medication complications, and very high triglycerides. However, that's just what most doctors will think of given that description, but of course there are many many more conditions with similar symptoms and it's very hard to know without labs/physical exam.
Did the doctors tell your family what was going on? what condition she suffered from? was she on the regular hospital beds or was she in the intensive care unit?
Again, I am very sorry for your family's loss and if you have questions, I will try to answer whatever I can.