Interesting and unnerving analysis of what could happen if Piggy invaded Greenland:

[Fiendish Thingy]

23. The mechanisms are in the constitution

You know how impeachment works, and yes it would take some time, but not as much time as Trump’s or Clinton’s previous impeachments. It probably could be done within 30-45 days under the extreme circumstances described above, if not quicker. Remember, impeachment is not a legal proceeding, and Trump’s typical delay tactics would not affect a truly determined congress.

If an order to invade was imminent, the 25th amendment might need to be used to forestall or countermand such an order. From Wikipedia:

Section 4. Whenever the Vice President and a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide, transmit to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office, the Vice President shall immediately assume the powers and duties of the office as Acting President.

Thereafter, when the President transmits to the President pro tempore of the Senate and the Speaker of the House of Representatives his written declaration that no inability exists, he shall resume the powers and duties of his office unless the Vice President and a majority of either the principal officers of the executive department [sic][note 2][7] or of such other body as Congress may by law provide, transmit within four days to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office. Thereupon Congress shall decide the issue, assembling within forty-eight hours for that purpose if not in session. If the Congress, within twenty-one days after receipt of the latter written declaration, or, if Congress is not in session, within twenty-one days after Congress is required to assemble, 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.

So, my reading of that section is the VP and majority of the cabinet can buy Congress at least 21 days to act. If the US were facing the cataclysmic consequences described in the OP, I think the motivation and momentum would be there. It’s very likely there would be some significant Sabre-rattling by the EU, Canada, Japan and others, both publicly and behind the scenes- for example, threats to sell off US treasury bonds, crashing the dollar, which would give Trump and congress advance notice of the conflagration that would follow an invasion of Greenland.

PS- I know how important word-parsing is to you, but I couldn’t find the phrase “immediately impeach and remove” in any of my posts in this thread.