It is hard to prove a negative but we do not have any sources that mention any public resistance or open rebellion against Queen Hatshepsut's rule.
Marc Van de Mieroop in his Egypt textbook A History of Ancient Egypt writes that the New Kingdom period is probably the one of best documented period of Ancient Egypt. We have surviving accounts from not only the countless royal inscriptions, monuments, and public documents but also from a surprising number of auto-biographies and journals of citizens, the richly detailed official accounts of military actions, legal documents and letters written by private individuals (e.g., Deir el - Medina), and surviving diplomatic correspondence.
In all this evidence that Egyptologists have available we do not have any mention of a mass public resistance against Hatshepsut's rule. If the absence of such an incident from official records makes sense the lack of even a hint from private accounts of individuals will not. That so even when she usurped Thutmose III's rule and established herself as the "King".
During her father's reign she held the powerful office of God's Wife.
She had taken a strong role as queen to her husband and was well
experienced in the administration of her kingdom by the time she
became pharaoh. There is no indication of challenges to her leadership
and, until her death, her co-regent remained in a secondary role,
quite amicably heading her powerful army—which would have given him
the power necessary to overthrow a usurper of his rightful place, if
that had been the case.
Today, we know Hatshepsut as a ruler famous for her many wars, restoration of ancient trade routes, and building projects.
- A History of Ancient Egypt (2011) Chapter 7, The Birth of Empire: The Early 18th Dynasty (ca. 1550-1390). Read specially, 7.2 and 7.5.
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