Some stuff I was thinking about families in GoT:
My guess is that GRRM has a fucked up family or something.

Other than arguably Davos and his dead son, it seems that there are no familial relations where anyone seems to share any personality traits at all.

Among siblings: Robb Stark is very different from Bran and Rickon. All the boys seem to have inherited Ned's bravery; Robb has some of the charisma but not the wisdom. That seems to have gone to Bran, who of course is now physically impaired. Sansa and Arya could not be more dissimilar.

The Baratheons: Robert, Renly, Stannis. Again, as dissimilar as three brothers could be.

The Lannisters: The same to a lesser extent. Jaime and Cersei, as incestuous twins, share cruelty and all three are rather cunning, but of course Tyrion's a drunken dwarf and Jaime is (was) one of the greatest swordsman of the realm.

Dany and Viserys: Dany is proving herself to be a bold and capable leader who inspires loyalty and love. Viserys was a sniveling fool and apparently didn't inherit the dragon gene.

Brienne and Samwell both hate their noble fathers.

The Hound and the Mountain hate each other.

I suppose it makes for more tension and better drama when there is infighting within families, but it also seems that GRRM was trying to say something about siblings and parents.