If there were a coup, maybe they could put the candidate who actually won the election (by 3 million votes) in the White House?
I really don't think the chances of a coup are high at all. I think there would be a lot of grumbling from Democrats (probably to a degree never seen before), and some from Republicans too, although not much; the rest of the GOP will back him to the end, or until their poll numbers and reelection odds take a serious dive (which would probably happen).
Trump's approval rating would go even lower (hard to imagine at this point, since he's already almost bottomed out). Pence would distance himself even more than he's doing now so as not to appear guilty of wrongdoing; Pence would also begin prepping himself to be sworn in as the 46th commander-in-chief.
I'm not sure what route it would take from there, but I do think that should Trump fire Mueller, his days as president are numbered. Should it happen prior to 2020, then he won't be a candidate for president in 2020. Either through impeachment, or just declining not to seek reelection, he would not appear on the ballot.
Also, Hillary Clinton would make another round on the airwaves telling the country, "I told you so." And she'd be right (again).
Move on. Hillary did not WIN the election. If she did, she would be in the White House right now. She knew the rules of the game (better than Trump) before she got in the race.