I don't remember any document defining possession of guns to be an inalienable right. While the 2nd Amendment uses the phrase "shall not be infringed", I don't see how that figures into the distinction you make between two kinds of rights.
OTOH, I do recall life and liberty being defined as inalienable rights (although in the Declaration of Independence, which has great moral standing but no legal standing), and as you can see in my post #33, the Constitution explicitly says that life and liberty can be taken from American citizens if done using "due process of law".
Do you hold, then, that the Government can take your liberty, your property, and your life, but it can't take your guns?
The "felons lose the right to vote too" argument is a falacy[sic].
I'm not sure what you mean by this. Do you dispute that felons lose the right to vote? Or do you think that the statement's true, but that it doesn't apply as supporting the argument?
Your first sentence is contradicted by your second sentence.
Right to bear arms: "...shall not be infringed." Period. That is made per the BoR "in order to prevent misconstruction or abuse of [government] powers". The Constitution made that recognition & protection when it went into effect.
Right to vote: interestingly, the right to vote was not even part of the Constitution originally (only vague references to the people choosing certain representatives). That was first added in 1870, prohibiting voting restrictions based on race, color or prior servitude (prohibitions on sex-based restrictions were banned in 1920). Note that the right to vote is Constitutionally only expressed in terms of what restrictions are impermissible.
The distinction between the right to arms and the right to vote is downright dramatic: one was embodied and protected in the original Constitution with "shall not be infringed", while the other was not even recognized at the federal level originally and was only added later.