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).
There won't be a coup. And even if there was, Clinton did NOT "actually win the election", despite getting more popular votes. Yes, the electoral college is stupid and should be abolished, but it's the rule in US presidential elections, and all candidates know that when they run. Claiming that a PV loser actually won is like saying that a losing football team actually won because they gained more yards than the winner; they may have gotten more in absolute terms, but they failed to get them where they needed to.
I also think that if Trump did fire Mueller, there would be some Congressional Republicans who wouldn't stand for it. Yes, some Republicans will be loyal to the end, but there
are some principled ones who I believe would fight Trump in this case (McCain, Corker, and Sasse come immediately to mind; I'm sure there are others.)
Message to Democrats: not all Republicans are scum. I know this may be hard to believe.
Message to Republicans: not all Democrats are scum. I know this may be hard to believe.