This is a little different than a traffic ticket.
I don't know if this woman and her son were aware of the deal struck with King Farouk, (I would presume on something like this they would do some level of research before saying, "Look what I found.") But the disparity between splitting proceeds with him and seizing coins from them is astounding. Also, they were clearly aware that their father sold some of the coins without charges being filed.
Like the fact that the U.S. Mint likely never had Farouk's coin in its possession? Like the fact that the settlement was a result of a legal battle?
As for the father selling some previously . . . totally irrelevant, from a legal point of view.
I suspect it comes down to laundering the provenance. Given the history, the woman must have known the coins were stolen, and therefore worth far less on the black market. But, by trying for an outcome similar to the Farouk deal (50% to the dealer, 50% to the Mint), she could realize a much greater amount in an above-board auction, with the ownership legitimized. She gambled and apparently lost.