So, the Constitution is pretty clear on this: if the Vice-President and a majority of the cabinet rule him to be incapacitated, then a message is submitted to the Speaker of the House and the President of the Senate. At that moment, the Vice-President immediately takes control of the Presidency, and Trump would be immediately removed from power. If he attempted to hold onto power regardless, the Supreme Court would likely hold an emergency sitting to make it clear beyond doubt that Vance is the President and that Trump no longer holds executive power.
Not quite. Once the letter is transmitted to the Senate and House of Representatives then yes, by automatic operation of the Constitution Vance becomes Acting President and Trump loses his power. However, the Twenty-Fifth Amendment also provides that if the President sends his own declaration that he is fit to undertake his duties then he, again automatically, regains the powers and duties of the office of President. Vance and a majority of the Cabinet would then need to send, again, a declaration that the President is not fit to discharge the powers and duties of the Presidency which would then kick the matter to Congress to decide by a 2/3rds vote of both Houses whether or not the President is fit.
It is not completely clear to me whilst waiting for Congress to decide the issue who is undertaking the duties of President. The draft might imply that the VP is Acting President during this time:
determines by two-thirds vote of both Houses that the President is unable to discharge the powers and duties of his office, the Vice President shall continue to discharge the same as Acting President; otherwise, the President shall resume the powers and duties of his office.
But equally you could read the Amendment as a whole as implying the President continue to be President whilst Congress is resolving the issue. Either way it would certainly get messy...