Accidental death policy?

I was once told by an elder law attorney that accidental death policies almost never pay out because the language is very specific on what constitutes a claim. Since payouts are somewhat uncommon, the policies are cheaper - which is why people buy them. I believe you that the accidental fall at the nursing home probably contributed to her death, but whether the law would agree with you is what you need to determine. Read the entire policy that you have and do some online lookups of the laws in your state. If you still think you have a claim, run it by an attorney. I don't know how long you have to file a claim, but I'd be careful about contacting the insurance company until you have your case together and you're sure about it. The insurance company is documenting everything you tell them and they will try to bait you into contradicting yourself. There's no such thing as an "off the record" or a "just wondering" phone call with an insurance company.

Unlikely, as she lived for more than 30 days after the fall.

You might want to talk to a lawyer but my gut feeling is the Insurance company will fight any claim. And they have more money and patience to fight it out where it will cost you money the longer it draws out.
Did your mom have a diagnosed heart condition? If not then you might "win"
If you have any indication from a doctor that she was declining due to the fracture of the hip that would help.
Did you file a suit due to the fall in the facility? If so the outcome of that might determine the outcome of your claim on the Accidental Death.