No, The Constitution Does Not Allow Cabinet Members to Remove a President
We may be in a post-constitutional and post-fact era, but the facts of the 25th Amendment are very straightforward.
The 25th Amendment was a response to the Kennedy assassination. Its goal was to formalize what would happen if the president becomes disabled. It is not a means to remove a president from office. Period.
The media has been talking up the 25th Amendment throughout the Trump administration. Most of these media claims should be dismissed as fake news. That said, any move to remove President Trump from office using the 25th Amendment would be an unconstitutional coup.
The Constitution provides a means of removing POTUS. That's impeachment. The 25th Amendment does not override or expand on that. And the Founding Fathers did not intend to allow presidential appointees to remove the chief executive. Nor, for that matter, did the 25th Amendment intend any such thing.
The Cabinet doesn't even exist in the Constitution. Cabinet members derive their power from the executive branch. It ought to go without saying that they have no independent power to override the executive.
But that's the unconstitutional administrative state we're dealing with.
Any talk of using the 25th Amendment in a non-medical scenario is treason and blatantly illegal. It's, in short, a coup. And should be treated as such.