I don’t think the President can fire anybody in the DOJ except the AG and Deputy AG. It’s not a situation unique to Mueller.
https://www.justice.gov/jmd/organization-mission-and-functions-manual-attorney-general
...The major functions of the DAG are to:
Exercise all the power and authority of the Attorney General unless any such power or authority is required by law to be exercised by the Attorney General personally...
...Be responsible for all DOJ attorney personnel matters, including final action in matters pertaining to the employment, separation, and discipline...
He can fire mueller. He can also order rosenstein to do it. Rosenstein has made his position clear