With or without the order by Thutmose III, the most motivated group at the time would have been his priests and administrative backers, who stood to profit most from a power grab. The long record of Hatshepsut's reign suggests a weak step son, who either dared not over take his step mother, or lacked the motivation. More than likely, the moment of seizing power would have been a long time coming, and Senmut's sudden disappearance and Hatshepsut's sudden fall from power, suggests a catalyst that energized the necessary momentum for a surprise coup. One overlooked potential cause was the discovery of Senmut's tomb under construction near the vicinity of his adored Queen. No commoner was considered worthy enough to be buried near the tomb of a Pharoah, and Senmut's endeavor would have caused serious shock waves. (It was never finished, never became his final destination, and his body was never found.) The intensely superstitious mindset of ancient Egyptians would have found this an intolerable affront to the good maat (kharma, balance of the universe) of Egypt. And it could have been just the evidence Hatshepsut's enemies needed to generate enough fast support to make a move.
Imagine the guard grabbing Senmut from his bed in the middle of the night, and making him a quick meal for the Nile aligators--not an uncommon solution for a quick disappearance. Hatshepsut would have woken in the morning to a world out of balance without her right hand man. Perhaps her denouncement would have taken place easily without a word from a mourning devastated woman. She was allowed to live out the rest of her life, as she died middle aged, and was mummified. But her proscription, and destruction of Deir el Bahri, was so violent, that this suggests, once more, the long powerful arm of Thutmose's priesthood, determined to prevent her from rising to the pantheon of Heavenly rulers, past Pharoahs, dwelling forever in the stars.