Not my words...

The question is does a right that belongs to the people to arm themselves (in conjunction with congress’s power to arm the militia) yield a stronger militia than if there were no right of the people to do so?

My personal opinion on this matter is irrelevant, it is the Constitution which is the relevant source of authority.

Again, is that clear enough for you?

These are the words of Patrick Henry from the Virginia Ratifying Convention, 5 June 1788--Elliot 3:51--52, where he directly quotes Article 1, Section 8, Clause 16:

Let me here call your attention to that part which gives the Congress power "to provide for organizing, arming, and disciplining the militia, and for governing such part of them as may be employed in the service of the United States--reserving to the states, respectively, the appointment of the officers, and the authority of training the militia according to the discipline prescribed by Congress." By this, sir, you see that their control over our last and best defence is unlimited. If they neglect or refuse to discipline or arm our militia, they will be useless: the states can do neither--this power being exclusively given to Congress.

Repeat:

this power being exclusively given to Congress.

From the same speech:

for, as arms are to be provided by Congress, they may or may not furnish them

The idea of the people arming themselves is not explicitly granted by the US Constitution. That power is exclusively given to Congress, which is the opinion of Patrick Henry based upon his reading of Article 1, Section 8, Clause 16, not my personal opinion.

The Second Amendment cannot contradict the US Constitution.

A law must be interpreted so as to be internally consistent.

Internal and external consistency

It is presumed that a statute will be interpreted so as to be internally consistent. A particular section of the statute shall not be divorced from the rest of the act. The ejusdem generis (Latin for "of the same kind") rule applies to resolve the problem of giving meaning to groups of words where one of the words is ambiguous or inherently unclear. The rule results that where "general words follow enumerations of particular classes or persons or things, the general words shall be construed as applicable only to persons or things of the same general nature or kind as those enumerated." 49 F. Supp. 846, 859. Thus, in a statute forbidding the concealment on one's person of "pistols, revolvers, derringers, or other dangerous weapons," the term "dangerous weapons" may be construed to comprehend only dangerous weapons of the kind enumerated, i.e., firearms, or perhaps more narrowly still, handguns. Here, the term "dangerous weapons" must be given a meaning of the "same kind" as the word of established meaning.

Thus the particular class (the Militia) defines the general class (the people) in this text:

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.