Dan- you have absolutely no obligation whatsoever to sell it. The family didn't stumble onto a "for sale" website, but instead your personal collection. I'm sure you've already explained to them the bat is not replaceable.
The only suggestion I have is maybe the next time an item comes up in an auction worth equal to or slightly more than your piece, you can contact the family and tell them if they can win that item for you, you would be willing to swap the bat for it. But that is entirely optional. Again, I see no moral quandary at all. The family may be disappointed, but such is life.
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