Complex sentence: Kate dismisses him, but as he continues to gather evidence for her she realises that he was right and goes on a crusade to find the truth, using it as a distraction from her problems with Mike, who now barely even looks at her.
Split into simpler sentences: Kate dismisses him, but as he continues to gather evidence for her she realises that he was right and goes on a crusade to find the truth. She uses it as a distraction from her problems with Mike, who now barely even looks at her.