particles - の versus が used to mark the subject of an appositive clause?

A friend of mine wrote this sentence in Japanese:

彼女のどんな困難からも逃げない態度を尊敬しています。
'Her attitude of not running away from any hardships is something I respect.'
'I respect that she has this attitude of always sticking to her guns.'

If I change the の here to が, would it be grammatically correct? If so, what would it mean?

彼女 が どんな困難からも逃げない態度を尊敬しています。