FauxPerspicacity said:
Doesn't secondary dominance have to do with playing chords of chords like a V of V chord in C major would be D major since the G is the V of C and D is the V of G.
Probably irrelevent.
I think that might have more to do with the actual scale form. In this case, the V of a scale usually is the Dominant Tone. The chords also use the same names (i.e. tonic, supertonic, median, dominant, subdominant, etc.)
As to leaving out notes of the chord (i.e. the 5) the chord is still established if the root or another note is doubled, as you will sometimes see in Classical music where it is not uncommon to see 3 root notes of a chord played and only one 3rd played. (This can result in an inversion of the chord, depending on where the 3rd is placed.) Deletion of notes often occurs when using 7th chords because of a lack of space for the chord. It's not uncommon to find chords structured with R-3-7-R.
By the way, you can also interpret the chord using A and C as a D minor chord with a minor 7th (DFAC).

Typically, though, the lowest note is usually assigned as the root of the chord.
The same ambiguousness can also be said of power chords (root-5) where the root is not doubled...it could be the root and 5 of a chord, but it could also be the 3 and 7 of a chord. What are the other instuments playing? What is your vocalist singing?
Remember, there are really very few chord forms and many of the chords that are found in Rock music are really just a rearrangement or renaming of chords. The easiest way to find out what a chord is is to take all the voices of that chord and arrange them until they form a perfect triad on a sheet (i.e. ACE, CEG, EGB, etc.) the lowest note will be your root. The chord will still retain its tonality no matter which way you scramble the notes - unless the bass note is a note that is not the root of the chord (then, it becomes one of the inversions).