Um, wow. I can't start to think how you go about this. It's like "Sorry about you're Mum and all that but how about (insert figure) for that old Gretsch kit?" The passing of her mother would possibly re-ignite the mourning of her father too. Particularly going through all the old photos and paperwork etc.
If you don't know the family very well, especially the daughter then the kit is gone.
Only a well phrased letter with a very generous offer, and maybe some sort of additional donation to any foundation the family are donating to might scrape you through with dignity. So you better really want this kit. No turning up and "Tyre Kicking".
She will at some point want to move the chattels on and that can be a big job in itself so you might just be lucky.
IT YOUR GAMBLE!