How can one deal with parents who approve of their daughter committing sins, such as working without hijab, dating young men, and traveling with them, and who threaten to withhold money from their son if he tries to stop her or inform the grandparents?

The parents who condone their daughter's immorality or incite her to it commit a grave wrong. Her father is accountable for her on the Day of Resurrection. Children are trusts given to their parents, who must raise them in obedience to Allah. Continue to advise your sister gently, warning her of Allah's punishment, and pray for her guidance. If you strongly believe that your grandfather can bring about reform, inform him cautiously without your father's knowledge to avoid his anger. You are not obliged to obey your father in not informing your grandfather if you anticipate a clear benefit from doing so. You can also arrange with your grandfather for him to observe your sister's actions and condemn them, as well as your father's, thereby removing the burden from you.