That wording is not in the Second Amendment. Here is what it says:
"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."
That wording is not in the Second Amendment.
You raise an interesting question, and I would love the idea of the 2A riding supreme over all the other Amendments, as the only one that applies to the laws of the States. But I've never heard of that as being the intent of the document, have you? The whole text of the USC seems to be a pact between the States (as representatives of their respective People), defining and restricting the powers of the Federal entity that will unite them, rather than the laws of the States.
What do comments from the time tell us about whether the 2A was considered unique in that way or not? You have me curious.