How can one deal with a wife who requests divorce and refuses to return, despite a religious fatwa declaring the previous divorce invalid, and with the marital relationship between them sometimes continuing, after a marriage that lasted 14 years and produced seven children?

If the Grand Mufti (definition) issues a fatwa (definition) that the divorce did not occur in the third instance, then your wife remains under your marital bond. She must obey you and return to the marital home. If she refuses without a valid reason, she is considered disobedient (nashiz), and it is permissible to discipline her as prescribed by Islamic law. If she persists, seek the help of wise individuals from her family to convince her. Otherwise, the last resort is divorce. You have the right to refuse to divorce her until she ransoms herself from you with compensation (khul').