These sorts of questions are fantastic when you come across them. And exploring ways to a solution can be very satisfying.
Yes and no.
The parent major scale is D. More soon.
The visual of the Circle of Fifths will help you find matching progressions in all keys. Hurray!
You have gone a little off track here.
Yes.
I’m afraid it isn’t that either Shane.
It is the 5th of the 5th. But …
It does not precede the 5th so it is not functioning as a secondary dominant.
Something else is happening.
The G major scale
G → A → B → C → D → E → F#
The diatonic chords
G → Am → Bm → C → D → Em → F#dim
The chord progression
| G | A | C | D |
As Roman numerals
| I | II | IV | V |
The A major chord is non-diatonic. It would be Am if only chords from the key were used.
A major = 1, 3, 5 = A, C#, E
A minor = 1, b3, 5 = A, C, E
It is the note C# that makes the difference.
C is the 4th scale degree in the G major scale. To play the A major, the chord built off the 2nd scale degree, the 4th scale degree has been raised - sharpened from C to C#.
There is one and only one place we need look for something with a raised 4th. It is to the Lydian mode.
The Lydian mode (or scale) is the same as the major (Ionian) scale except for one difference, it has a #4.
The G major scale
G → A → B → C → D → E → F#
The diatonic chords
G → Am → Bm → C → D → Em → F#dim
The G Lydian scale
G → A → B → C# → D → E → F#
The diatonic chords
G → A → Bm → C#dim → D → Em → F#m
I mentioned that D is the parent major scale. And here we can see that. Look at G Lydian. It has two sharps - C# and F#. That is an exact match for the D major scale. Look at the diatonic chords of G Lydian - they are the same as those in the key of D major. G Lydian is a mode of the D major scale.
Aha.
The A major chord is a Major II chord in the key of G.
It is a borrowed chord.
The term ‘borrowing chords’ is an easy means of describing something that music theory allows us to analyse. A term with an equivalent meaning, perhaps a more formal term, is ‘modal interchange’.
Modal interchange applies when one or more chords are taken from a mode of the same root note (a parallel mode). This need not be limited to the parallel minor key but can be any of the seven modes.
This song borrows a chord from the G Lydian mode.
If the progression was
| G | C | A | D |
or
| G | A | D | C |
then it would rightly be seen as a secondary dominant. Because it directly precedes the V chord of D major.
For more about borrowed chords and using the Circle of Fifths: Using borrowed chords - introduction + examples
For more about modes (including some Circle of Fifths also): Modes Parts 1 - 9
All of which reminds me …
I had promised long ago to extend my series and write a full topic about secondary dominant chords.
One day, when time allows.