Am I understanding you properly, are you saying that Martin gives too much in to political correctness by liking Arya and Tyrion too much? That he has Invented these characters out of fear for being seen as politically incorrect, with all those Lords and Ladies, so he needed the "physically challenged" cripple in the story? In that case Martin could have done better: he could have made Tyrion the good guy without flaws who is always wronged against and never wavers in doing good deeds. Mission in political correctness not accomplished here! The guy is simply too much of a human being to be the alibi cripple for our bad conscience.
And Arya? Is it politically incorrect to invent a politcally correct character, while promoting the politically incorrect girl would be the new correct? Should Martin promote the female agency to live an allegedly feminine life within the frame of conventional expectations towards women?
And this is what Sansa's story is all about. By the end of AFFC she specifically says I do not want to marry again, and laments that no one will ever lover her for herself only her claim, which is a complete 180 from where she started. Yet some readers still view her as passive and weak even then. I disagree but that is my personal opinion there. So, for me it's not about that Arya's way of rejecting being feminine and following "manly" pursuits is the better way, it's just a different way that works for her, but that doesn't mean that Sansa's way is less legitimate or strong a statement. However, I believe that our modern society stuffs down our throats that Arya's way is the better way. For ex, Disney was mentioned earlier and Disney's most recent animated release, Brave, is the perfect example of it. I won't get started here on why I dislike this movie as this is not the thread for it but suffice it to say I gritted my teeth through most of it, and hated how they ended the conflict between the traditional mother and the spunky daughter who is oh so great with an arrow, which is that the mother basically gives in!)
Anyway, I actually commend Martin in that he seems to be examining these issues from all different angles. Catelyn is a strong mother type, who acts on emotion. Even Cersei has strong maternal feelings and is motivated in her own twisted way by the need to protect her children. Another real good example is Brienne. Though Brienne has learned to fight and dress like a man, she only does this because she believes that is her only option to have some relevancy in this world. If you look at her thoughts throughout AFFC, she actually seems very feminine in her thinking and seems to want to get married and have children. She develops a touching motherly relationship to Pod and she would make a great mother. So, is Brienne making the strong feminist statement then? Well, yes in that by dressing as a knight and learning to fight she is saying screw it I don't need to get married, but no, in that she seems to have given up hope of ever having something she truly seems to want, to be married to a man that she can love and to have children, which is a sad thought if you think about it.
I am trying not to give my personal opinion in this little feuilletonistic political essay. what I am trying is to make you aware of the general weight of this conflict for us women. We are at a fork in the road for women here. This can be seen e.g. in my country by bringing topics like the nature of motherhood and childcare back on the political agenda.
Now getting back to the OP, Martin appears to have stated that Cat and Sansa are his least favorites, but I don't get the sense that he hates them. I'm pretty sure I read another blurb from an interview he gave where he said that he loves all his characters as they are like his children, his creation, and it's hard for him to write when he has to kill one off. I also know I read an interview with him recently somewhere where they discussed Cat in particular as being a strong woman that seemed unusual in this genre and Martin agreed. (Don't have the comments directly at hand though so I hope I represented these comments correctly). So, I am giving him the benefit of the doubt that he structured his story in such a way as to make each character's journey a study in development even if at times he seems to have had some trouble with it, for example the extreme naivite of Sansa in the first book.