Article II of the Constitution grants Congress the power to impeach “the president, the vice president and all civil officers of the United States.” The phrase “civil officers” includes the members of the cabinet (one of whom, Secretary of War William Belknap, was impeached in 1876).
Impeachment has to have either a felony (you dont impeach for traffic tickets) or a twisting of the public trust. It probably isnt going to be used for an appointee, as it is insanely hard to do and most will just resign before it gets that bad.
Because you are asking about impeachment, you are aware that you need the House to investigate and vote, with a majority, and the Senate to vote with a supermajority. Very hard to do if out of power. Your first job is to not be seen as attempting a coup. The American people do not reward parties that attempt coups.
All very true. The people will approve a change of party via election but not via impeachment and conviction.