Well, if their relative stole it then they should have to give it back. If not then they should be able to keep it.
They don't know that the coins were stolen. The guy was a licensed dealer, and at the time, he was permitted to trade bullion for coins from the treasury.
Certainly a reminder to keep your mouth shut about some things.
Makes no difference. The coins were never monetized when the order to melt them was issued. As a result all double eagles of that mint year (except one) were destroyed.
Or looked at another way, it is the mint's gold as the coins were never issued as money. Therefore they are stolen government property. Wether the family knows it or not, stolen property, when found, is always returned to the legal owner.