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Graycn,
First, the scenario you described is not at all what I had in mind when I said it wouldn't be worth the effort of scanning a book just for your own use.
Regarding this particular issue, your first step should be to identify the individual who controls the rights. You talk about the "family". The person you should be looking for is the literary executor of the author's estate. If no such person was appointed when the author died, then it is the general executor, or any remaining beneficiaries (the person or people who now control the rights).
You've got to identify the person in question, and then contact them to discuss some kind of arrangement for sharing the book in the way you have in mind. Obviously, no-one can say whether they are likely to agree, or what you should offer them, without knowing more about what the book is worth and what the demand is likely to be.
If you can't locate the appropriate person, you could try contacting the original publishers, if they still exist. It's almost certain they would have a record of the literary executor or beneficiary of the estate.
Good luck with this. It will be interesting to hear how you get on.
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