It was not their property to "reclaim".
Are you insinuating that that was a cause for Lincoln to initiate the invasions of Sumter and Pensacola, call up troops, and declare a blockade?
There was no "invasion" of Sumter and Pensacola - why would they need to invade properties that belonged to them?
That is truly farfetched(sic).
Many of your notion are...
Incorrect.
Most of the various military and federally occupied locations had originally belonged to the states, and in the case of Ft. Sumter, the State of South Carolina.
The actual fort was erected by the Federal Government under the Constitutional guarantee of protection from invasion.
In this regard, under the related article against "denial or disparagement" of the claims of any state, the Federal government had no more claim to the territory than some pecuniary interest in the materials of the Fort itself.
It is likewise guaranteed in Article IV, Section IV that the United States could only involve itself militarily within a state on application (and approval) of the State's legislature.
Once Major Anderson moved from Ft. Moultrie, he was involving his forces in the sovereign and independent actions of the State of South Carolina. The same was true in the event of the appearance of the "Star of the West" and the "Harriette Lane", both Federal warships attempting to interrupt the protected intercourse of the state of South Carolina.
As such, South Carolina was entirely within its rights as a sovereign state to order foreign aggressors from its borders, and to use whatever reasonable force was necessary in order to do so.