No person shall be ... deprived of life, liberty, or property, without due process of law.
The due process reminder can't be insinuated into the argument often enough, imo.
I tend to agree with those who say these coins were stolen in the first place and that, therefore, the gentleman's children ought not to be allowed to claim ownership. However, that's neither here nor there; due process is an absolute right, even for criminals (and their children), and the gov't is clearly trying to circumvent that requirement in this case, imho.
Plus I have a nagging suspicion that there ought to be some kind of statute of limitations on this kind of "loss." Nothing more obscene than the Spanish crown trying to claim rights to a galleon full of looted treasure 500 years after it went down.