Mutnodjmet ("Sweet One of Mut") is the sister or half-sister of Nefertiti, this is certain. One inscription reads "Mutnodjmet, may she live like Re forever, sister of the King's Great Wife, Nefernefruaten-Nefertiti." But, 'sister' could either be full sister or half-sister. Mutnodjmet also appears to be the daughter of Ay and Tey, because the young Mutnodjmet feature quite prominently in Ay and Tey's tomb at Amarna.
The Queen's Mother and the God's Father
Queen Tiye's parents were Yuya and Thuya, two commoners who were given the great honor of being buried in the Valley of the Kings. They were, most likely, also the parents of Anen and Ay. Thuya often said that she was the 'Queen's Mother' in fact, she showed off the title quite a bit in her tomb. Yuya, however, never said a word about being the father of the Queen, but he did have the title, 'God's Father' which many feel should be translated as "Father-in-law of the God," the 'God' being the Pharaoh. This is important if we are to figure out the parentage of Nefertiti.
Ay and Tey
These are the parents of Nefertiti's sister/half-sister, Mutnodjmet, so at least one of them is a parent of Nefertiti, let's figure out which. No where does Ay claim to be "The Queen's Father" like Thuya claimed to be "The Queen's (Tiye) Mother" and Tey claimed to be the mother of Mutnodjmet. But, like Yuya (a Queen's father) before him, he does take the title "God's Father." So Ay is, in likelyhood, the father of Nefertiti, since he takes a title that seems to mean "Father-in law of the Pharaoh", the Pharaoh being Nefertiti's husband, Akhenaten. But is Tey her mother? It doesn't look like it. She never claims to be the mother of Nefertiti, only her 'nurse'. This seems to imply, that although she did not give birth to Nefertiti, she did raise her.
The Most Likely Conclusion
The most likely conclusion would be that Ay was married twice. The first wife was the mother of Nefertiti, and she died either at, or shortly after, the birth of Nefertiti. Ay re-married, this time we do know the lady's name, Tey, and she acted as the infant's 'nurse' and also gave Ay another daughter, Mutnodjmet. This would make Ay Nefertiti's father, Tey her step-mother, and Mutnodjmet her half-sister, and all this fits the evidence quite nicely.
Nefertiti most likely married Akhenaten (then called Amenhotep) when he was still the Crown Prince. Before the couple changed their names, she would give her husband three daughters: Meritaten, Meketaten, and Ankhesenpaaten. Shortly after the birth of Ankhesenpaaten, the couple became Neferkheperure-Wa'enre Akhenaten and Nefernefruaten-Nefertiti. It seems Akhenaten's Great Royal Wife played a vital part in his new religious regime; she is often shown taking an active role in the offerings and rituals to the Aten. It is likely that Nefertiti played the role of something like a hig priestess in the new religion. Some have even suggested that she, the Aten, and Akhenaten represented a divine triad; Aten being the father, she being the female aspect, and Akhenaten being the male aspect. But this is still theory, no text has been found to prove this.
Nefertiti's Disappearing Act
After the moce to Akhet-Aten, Nefertiti gave birth to three more princesses. Nefernefruaten ta-sherit (who was named after her mother), Nefernefrure, and Setepenre. Nefertiti was present at the death of Meketaten, she is shown there mouring the loss of the second princess with Akhenaten, Meritaten, Ankhesenpaaten, and Nefernefruaten ta-sherit. Nefernefrure and Setepenre are missing from the scene and either: a) already have died; or b) were deemed too young to participate and were not drawn in the scene. But soon after this tragic event, Nefertiti ceases to be mentioned. Her names and titles are erased and replaced with those of Meritaten and Ankhesenpaaten. What happened to Nefertiti?
Fell from favor...?
Some have suggested that Nefertiti fell out of favor with Akhenaten. Many reasons have been suggested, from an affair to questioning Atenism, even (ala Henry VIII) for the failure to give Pharaoh a son. She may have continued to live, in relative obscurity, in the northern part of the city. Some even suggest that she lived all the way into her son-in-law, Tutankahten's, reign.
Others have proposed that Queen Nefertiti ceased to be mentinoed because she had become a king. Ankh(et)kheperure Nefernefruaten is thought, by some, to be none other than Nefertiti. But Ankhkheperure was also the prenomen of Smenkhkare...
Or maybe, Akhenaten's beautiful one just passed away. It is by far the simplest explaination, but not the only one. Maybe she died in childbirth, or of an illness. Perhaps it is the enigma of Nefertiti that draws so many to her, or perhaps it is her serene beauty, preserved forever in that famous bust by the magnificent sculptor, Thutmose.