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If called to arms by the President, they would be armed like/by the National Guard and/or requested to bring their own guns. The unorganized militia is also known as the reserve militia to the Guard. Hopefully there is never an invasion severe enough to call the entire country to arms, but it is 100% possible.
Everything is a law that can be changed, even the Constitution. It takes more to change certain laws, like the Constitution, and the Constitution prevents certain things from being part of laws. If you disagree with the 2nd, convince 75% of the country you are correct and we can change the law.
I hate to break it to you, but yes, the President does have that power as the Commander in Chief. Multiple States also have the same codified in State law, and the Governor can do so as well. There are prescriptions for both volunteer requests from the unorganized militia, as well as drafting them as well.