Isn't that the whole idea behind the US second amendment to enable citizens of the US to rise up against their own government when they disagree with the elected government?

That seems to be one part of the motivation that the founders adopted the 2nd Amendment. It's certainly supported by some quotes from Thomas Jefferson.

However the idea that the primary motivation for the 2nd Amendment is to enable citizens to rise up against the US government is vastly overstated. It mostly seem to be an idea popularized by the American right.

Probably a bigger reason for the 2nd Amendment was to facilitate the defense of the state, rather than it's overthrow. Consider the Oath of Allegience that is taken by new citizens, members of the military, and many public officials that pledges to defend the Constitution against all enemies foreign and domestic.

There's little reason to think that the founders were particularly interested in enabling the public to rise up against the new government they were busy creating. The founders even included in the Constitution the provision that Habeas Corpus could be suspended "when in cases of rebellion or invasion the public safety may require it". That hardly seems to suggest that rebellion against the government was seen as a right.

During his first term George Washington raised militias from various states to march on western Pennsylvania to quash the Whiskey Rebellion. You have to consider at the time that many of the founders did not want or expect the US to create a standing army, and so would need to rely on raising citizens militias to defend the state.