I'm not sure that I fully get your question, which is probable because I don't have enough theory knowledge or experience playing with people.
For the key of G, the chords in the key are G, Am, Bm, C, D, Em and F#dim. For all major keys the short hand for the chords in a key is often written as I, ii, iii, IV, V, vi, vii[sup]o[/sup], where the Roman numerals represent the note's position in the scale, the capitals mean it is a major chord and the lower-case means it is a minor chord. When the key is minor (from memory it can get more complex because the notes in the key can change on the way up and down and so there are additional chords that can be added - but that's a different story

So in the key of C the chords are C, Dm, Em, F, G, Am and Bdim.
Relative minor, I think, means the minor key that has all the same notes as the chord it is related to. So for C the relative minor is Am (which has no sharps or flats). It is the sixth note in the scale. In the circle of fifths diagram, the relative minor is the chord/key on the inside of the circle.
So if you take the sectors on each side of a key and the sector for the key in question (the quadrant as Ness calls it), it has six of the seven chords in the key. It's so cool.

I'm sure someone else can answer the rest of your question, or correct me if I'm wrong or I've misunderstood.
Shel