When I was three years old, my dad received a notice from our local interpretive center banning him and his children from the premises. This museum is federal property, coordinated and overseen by US fish and wildlife and the Corps of Engineers. We were banned in 2002, and in 2015 my dad was sent another letter lifting our ban. I was 16 at this time. Is it lawful to ban a minor from federal property?
Banning you from the museum raises questions about your due process, equal protection, and First Amendment rights.
Generally speaking, a person banned like this would be unlikely to collect any damages, but may be able to obtain injunctive relief to prevent the museum from enforcing its ban. Of course, it would depend on the reason for the ban and the procedures the museum went through in imposing the ban and permitting you to challenge it.
In your case, though, the ban has already been lifted, so there's probably not much room for any kind of legal action.
EDIT: Since there are several people contesting -- with no law to support them -- the validity of this answer, here's a case discussing the First Amendment implications of access to museums:
As a limited public forum, there are certain First Amendment activities permitted on [National Civil War Museum] grounds and others that are not. For example, lectures or programs on a Civil War topic authorized by the museum and the public's attendance at these activities would be permitted uses, but activities concerning other topics (including the immorality of homosexual activity) would not. Diener v. Reed, 232 F. Supp. 2d 362, 385 (M.D. Pa. 2002), aff'd, 77 F. App'x 601 (3d Cir. 2003).
You can no longer sue.
The ban was lifted, suing to have the ban lifted is moot.
Also note, that the end of the ban is more than 5 years ago and started 18 ago. That matters for the ability to sue too: the statute of limitations is often far shorter. I think whatever claim might have existed is now no longer available due to the statute of limitations.
As an example, relief under 42USC1983, in general, has no statute of limitations in the text, but whatever it is, it starts to run when the violation happens or the injured should have known about them - which was 18 years ago. In Wilson v Garcia SCOTUS determined that 3 years was appropriate in the discussed New Mexico case, and to use the state statutes of limitations for personal injury of the state the action happens in. In Shorters v Chicago the SCOTUS decided 5 years was appropriate as that was the general Illinois statute of limitations.
If you could sue it would have to broadly for one of two reasons:
Did the museum deny some specific right, as for instance the family had a season ticket granting repeated access which they refused to honour?
Did the museum cause damage, real or reputational? Did they for instance, unreasonably publish the ban, which might in some circumstances be libellous?
My guess would be that lifting the ban might remove any claim for lost rights.
I don't think lifting the ban would relieve them of responsibility if, for instance, they had damaged your research career by suggesting you were not a fit and proper person to be allowed entry to the museum.