How we cite our quotes:
Plots have I laid, inductions dangerous,
By drunken prophecies, libels, and dreams,
To set my brother Clarence and the king
In deadly hate the one against the other;
And if King Edward be as true and just
As I am subtle, false, and treacherous,
This day should Clarence closely be mew'd up- (1.1.1)
Richard's first mention of his relation to his family prepares us for the way family will function in the play. Richard speaks of deceiving one brother to imprison the other. He even explicitly compares himself to his brother Edward, saying that he is all the evil that Edward is not. Thus we get the hint that family will not be about the ties and the love that bind people. Instead, it's just one more instrument Richard will use to manipulate and spread his hate.
He that bereft thee, lady, of thy husband
Did it to help thee to a better husband.
His better doth not breathe upon the earth.
He lives that loves thee better than he could.
Why, that was he.
The self-same name, but one of better nature.
Where is he?
Richard implicitly draws a comparison between himself and Anne's dead husband, the murdered Prince Edward, by pointing out their old family connection. By invoking the Plantagenet name, Richard goes far back to the original family from which the two warring houses, Lancaster and York, sprang. Amidst all the animosity in the play, it's easy to forget that the warring Lancasters and Yorks are actually related by blood (hence the dispute). Remembering the family connection between the Lancasters and Yorks also makes all the quarreling within the York family a bit more understandable. Being family doesn't guarantee allegiance. Fighting within the family is common, hence the Wars of the Roses.
What, were you snarling all before I came,
Ready to catch each other by the throat,
And turn you all your hatred now on me?
Did York's dread curse prevail so much with heaven
That Henry's death, my lovely Edward's death,
Their kingdom's loss, my woeful banishment,
Should all but answer for that peevish brat? (1.3.10)
Margaret represents the old guard that the Yorks defeated to come to power. As they turn from their in-fighting to attack her, we get a rare glimpse of family loyalty and unity amongst those related to King Edward.