I actually would love a more accurate depiction of Hatshepsut's story. It wouldn't be boring at all. Real-like Hatshepsut was a shrewd schemer, not naive and sheltered like this manga makes her out to be. When she was still a child, her father Thutmose I appointed her God's Wife of Amun, the highest-ranking priestess in the cult of Amun. Hatshepsut took advantage of that key position to bring the cult of Amun to her side. So, contrary to what this manga would make you believe, the priests of Amun weren't her enemies; they were her biggest supporters, and they were instrumental in her rise to power. All this is missing from this manga.
After Hatshepsut became pharaoh, she couldn't hold the position of God's Wife of Amun anymore, so she appointed her daughter Neferure as God's Wife of Amun because she needed someone she could trust in that key position. That's also missing in the manga. Additionally, there is no evidence that Neferure was ever supposed to marry Thutmose III.
That been said, it is accurate that when Hatshepsut became pharaoh, Neferure took the queenly role. She was given the titles Lady of Upper and Lower Egypt and Mistress of the Lands. Titles that belonged to Hatshepsut before becoming pharaoh.