I'll take a crack at it...
The relative diminished chord is the chord you arrive on by taking the 3rd of the dominant:
i.e. the relative diminished chord for Bb is found by taking the third of the dominant, F,
which gives us A diminished.... so A diminished is the relative diminished of Bb
But if the chord is the
dominant of the scale, then we find the relative diminished by taking
the third of the root of the dominant:
i.e. in the key of Db, the dominant of the scale is Ab... and the third of Ab is C... thus
C diminished is the relative diminished of Ab in the key of Db
Now once you find the relative diminished chord, you then lower all the notes by a chromatic to
arrive at the diminished family of roots to build your triads on:
i.e. since the relative diminished chord of Ab in Db major is C Eb Gb A, we lower each note by a
chromatic, arriving at B D F Ab ... and we then use each of these notes to build our triads in
the right hand, over the left hand shell (which in this case is an Ab shell)
The notes are called a family first of course because diminished chords built on any of the 4 roots
give the same chord, and also because we are using these same roots to build other triads to
create these interesting voicings.
That's it!
Hope it helps

..... Diverse and Sjonathan... how'd a brutha do?
Eggs