Besides impeachment (and please be clear, this question is NOT about impeachment), there is another constitutional way that the
president can be removed from office against the president’s own will. What is that procedure, and exactly what is the sequence involved? (Your answer does not have to include time frames, but it does have to be very specific about who does what.)
Yes, there is. The 25th amendment to the Constitution can be used to remove the President, in the case that the President becomes unable to fulfill their duties, in the sense that they are physically incapable of doing them. This doesn't have to do with laziness or disagreements on policy, but with a President's mental fitness to actually do the job. The process works with the Vice President and a majority of the Cabinet voting to relieve the President of his or her duties, and then the Vice President takes the office of President. But after this, if two thirds of both houses of Congress do not vote to uphold the decision by the cabinet within 21 days, the powers and duties of the President are transferred back to the President, and taken away from the Vice President.
Checks and balances is where each part of the government can "check" each other. This is to ensure that no branch of government becomes too powerful. An example of this would be the President vetoing a law passed by the Judicial Branch.