When faced with a difficult situation, kate ensures that she has the final word, even if she forcefully has her way. which kind of conflict resolution approach does kate follow?

I believe that Kate follows the conflict resolution approach known as competing.
It means that she will compete with everyone else for power, and stand strong in her decision to win - and she will win in the end, regardless of the consequences or how she achieved her goals. Sometimes this approach is good, but not always.