Was Cleopatra the mother-in-law of Tutankhamen?

No Tutankhamen was son of nefetti he was Egyptian pharaoh of the 18th dynasty (ruled ca. 1333 BC – 1323 BC) Cleopatra was was a member of the Ptolemaic dynasty, a family of Greek origin that ruled Egypt after Alexander the Great's death during the Hellenistic period born about 69 BC so only 1200 years between their lives, are you getting confused with tutankhamens mother Nefertiti 1370 BC – ca. 1330 BC

During Akhenaten's reign (and perhaps after), Nefertiti enjoyed unprecedented power. co-regent with her husband equal in status to the pharaoh. It is possible that Nefertiti is to be identified as the ruler named Neferneferuaten. Some theories believe that Nefertiti was still alive and held influence on the younger royals. If this is the case, that influence and presumably Nefertiti's own life would have ended by year 3 of Tutankhaten's reign (1331 BC). In that year, Tutankhaten changed his name to Tutankhamun. This was evidence of his return to the official worship of Amun, and his abandonment of Amarna to return the capital to Thebes.[2]