Is the sister who took gold from her deceased father required to return the right to her brothers or to her father, and what should she do to clear herself of liability?

It is not permissible to take from a father's wealth except with his permission. It is obligatory to repent and return the gold or its value to the heirs. You are entitled to your share. Giving charity or performing 'Umrah on behalf of the father does not substitute for returning the wealth to the heirs.