Sansa's problem is not that she trusted her father, who killed her dire wolf, but that she lives in a fantasy world thanks to the stories of Septa Mordane. Sansa believes everything she was told about knights and royalty being noble. This is shown very well in the books, and yes, at times it was very boring to read about her character. In the TV series, they have had to cut a lot of her character building, but they still have done a good job of showing that she is starting to realize not all the stories are happy, and not all knights are righteous.
As to Cat, while she understands more about how things work than her children, she too set things in motion for the fall of Winterfell by not being there. She never truly loved Winterfell and her marriage to Ned was one of duty and honor. She only learned to love Ned later. The way she treated Jon was harsh and some would say uncalled for, especially if she loved Ned.
So Cat is not without her faults, but she is no dolt .
Of all the Stark Children, Arya and Jon seem to be the only ones with any sense. Bran is very much like Arya, adventurous and full of questions. Had he not met with his accident, I think he would be a very different character in the books.
To me Dani is more like Sansa, just older and with a little more knowledge of how the world works. But she too is a dreamer, like Sansa. Both have big hearts and want to believe the world is not as evil as it appears. Both are getting lessons otherwise...
