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Actually, the founders did have the foresight for including something to deal with the installation of an illegitimate president, or any other tyrannical/lawless portion of the government:
A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

A less dramatic answer is to impeach, convict and remove an illegitimate person occupying the office of the president.
The Confederate States of America tried the rebellion route and it didn’t turn out too well for them. They ended up occupied, disbarred from citizenship and forced to accept the very provisions of societal change that they were rebelling against.

Not quite; there is a huge difference between the single [debatable] State’s right of secession and the definite Contra-Constitutionality of all three branches of the government.

Consider TARP & ObamaCare; legislative nightmares so contrary to the constitution that it should make you sick.
Consider the USSC/Judiciary’s tyranny & on-the-fly modification of the Constitution: the “commerce clause” being applicable to INTRA-state commerce, the shredding of the 4th Amendment by allowing no-knock warrants & warrantless searches, the virtual repeal of the strictures the 5th Amendment placed upon eminent domain, the super-legislative powers they exercised in Roe v. Wade...
Consider the refusal of the [federal] government to address the issue of the invasion of AZ (as required by Art 4, Sec 4).

IOW, ALL THREE branches of the Federal government are demonstrably contra-constitutional. No if/ands/buts, they are a monster that *will* cause bloodshed, one way or another.

A less dramatic answer is to impeach, convict and remove an illegitimate person occupying the office of the president.

Which is a near impossibility when the jury in this situation is as corrupt as the usurper whom they protect.