Is it permissible for a person coming from Jeddah to visit his family in Mecca and his wife to enter into a state of ihram for Umrah from Al-Ji'ranah on Saturday?

If you intend to perform 'Umrah while on this journey, then it is obligatory for you to enter into the state of ihram from Jeddah, because Jeddah is closer to Makkah than the miqat. This is based on the Prophet Muhammad's (peace be upon him) hadiths: "Whoever is within these boundaries, his place for ihram is from his dwelling... even the people of Makkah enter ihram from it [Makkah itself]," and "Whoever is within that [the boundaries of the miqats], then from where he originates, even the people of Makkah from Makkah." Furthermore, Sheikh Ibn Baz clarified that Jeddah is a miqat for its residents and those residing there, and the fatwas of the Permanent Committee concurred with this.