well, I know Peter was rash in the battle in the movie but the book doesn't tell us if he was rash or not. Even so, he was already in the middle of a battle and he would have had to fight the witch at some point. He was just rushing it a bit. With Tirian its at the beginning of the book when the dryad comes and tells him the trees are being cut down. And instead of going back to the castle like he should have and made a plan, Tirian just took off with Jewel to fight the Calormenes. Very stupid decision on the part of a king. No matter what, you have to consider the well being of the entire country. I"ll try to find the passage for you.