I have followed this story since the start, and actually the family has been pretty shrewd about handling it. There was no doubt the coins were real, but they would be seized by the government if there was any attempt to sell them. The one and only 1933 Double Eagle that IS blessed by the government to be in private hands was first seized in a sting operation when it was being sold in a private transaction. So the family had no opportunity to do anything unless the coins were ruled legal to own.
Handing them over for "authentication" provided a way to get a court to rule that the government could not prove they were stolen, and that would open the door to being able to sell them openly (realistically, they might go for $2-3 million each, not $8 million). They knew the government would not give the coins back, so they could go to court to force the return of the coins. If that happened, that would then resolve the "legal to own" issue.
The family has some very smart expert witnesses on their side, who have done extensive research in the National Archives. They believe they can show there was a window of time where the coins could have been legitimitely obtained from the Mint prior to FDR's order to stop issuing gold coins, and have government documents to back it up. They don't have documents that prove that the coins were obtained legitimitely, but they believe they can show it was possible. If they can create that reasonable doubt, they might win.