You can’t equate a private property right with the states rights. The State “owned” property is actually the collective property of the people and it’s legislative use has been, in the past, strictly defined and then subsequently “regulated” by unconstitutional acting or mandated bureaucracies and the latter instances are almost ALWAYS done to further the interest of some type of connected individual or corporate or organizational interest.
Private property is just that, private.
Sorry, you are incorrect.
Private property rights deals with the right of the owner (be it an individual, corporation or state) having the right to determine the use of that property. This is in contrast to squatters rights which follows a collectivist view that the needs of the many are more important that the owner and thus, the group can take from the owner.
State’s rights deal with the enumeration of powers in the Constitution and those powers not enumerated being reserved to individual States.
Regulation of land owned by the federal government is one of the enumerated powers in Article 1 section 8 of the Constitution. So your assertion that such regulation is unconstitutional is demonstratively false.