I mean to be clear, there is nothing special about the White House that magically makes the occupant of it President. It's simply tradition.
If you impeached Trump, and he refused to go, you could in fact just set up the federal government someplace else.
But again, at some point the generals are gonna get two phone calls, from two people claiming to be President, and they are gonna have to pick one. And well, fucked if I know how THAT story ends.