Am I right in cutting ties with my adulterous cousin who insists on her actions after being advised?

One must be cautious not to accuse others of adultery without proof, due to the severe implications of slander (qadhf). If it is proven that your cousin is committing adultery, she is in grave danger. You have done well by advising her, and you should continue to advise her gently and pray for her guidance. If advice does not work, you can threaten to inform her guardian. If she still does not desist, it is advisable to ostracize her if doing so serves a greater benefit.