If it is difficult for the master of the house to go to the mosque, and he is hosting a pious Hafiz, then who has more right to lead the prayer: the master of the house or the guest? And has anything been mentioned about this in the Qur’an or Sunnah?

The host (owner of the house) has more right to lead the prayer in his house than others, even if others are more knowledgeable and فقيه (understanding of religious law), provided that the host is qualified to lead the prayer. Some scholars have recommended that the host present someone better and more knowledgeable than himself, citing the Prophet's (peace and blessings be upon him) saying: "Whoever visits a people, let him not lead them in prayer; rather, let a man from among them lead them," and his saying: "A man should not be led in prayer in his own house or in his domain, nor should one sit in his place of honor except with his permission."