The spoiled, selfish brat was Arya! Look at the Stark girls back in season 1, Sansa was a bit stuck up and naive and dreamed about the south but it was her fathers choice to have her marry Joffrey and make her a princess/queen, after that decision had been made she played the role she was supposed to, that of a good (future) wife.Then you're giving her WAY more credit than I ever have. She's a spoiled, selfish brat. Always has been. She did what she did in S1, not to avoid conflict, but to make sure that she got her chance to play princess/queen.
Ned even defended Sansa not telling the truth about Joffrey because unlike Arya he realized that she was in a difficult situation, what was she supposed to say, "Joffrey started it because he's a little shit and then he cried like a bitch after he lost!"? That was not an option, as his future wife Sansa was supposed to be loyal to Joffrey, she also wanted to be loyal to her family so she did the best she could in that situation, she claimed not to remember so that she didn't have to blame anyone. If she was as selfish as you claim she could have easily sided with Joffrey, she didn't do that, she was very aware of the situation and her position.
And Arya? Like I said above, she was the spoiled, selfish brat. She did what she wanted, disregarded all expectations of society, was disrespectful and rude and she got away with it because her father was top dog in the north. She continued to act like that even when the royal family was around, she didn't care about them or their position, all she cared about was what little princess Arya wanted and she certainly knew how to act like a princess even if she didn't look the part like when the guards wouldn't let her into the red keep, she was VERY quick to point out that she was Arya Stark, her father was hand of the king and demanded to be let in immediately.
In stories like this the tomboyish girl always seems to be more popular and appealing than the girly girl who wants to get married and have babies even if the tomboy is kind of a bitch.