Hypothetical...Sanders runs as independent

Sanders runs against Trump and Clinton…the election gets thrown to the House of Representatives… Would the Republicans fall in line to elect…Trump?

Probably. They’re not going to make Hillary or Bernie president. If they go rogue and try to go outside the box they’ll just split their own party and the Democrats will join up to put Hillary through, or Bernie if he’s got enough of the popular vote behind him, but that seems more unlikely than the scenario in the OP.

Remember, though, that the rules for such a House vote are very idiosyncratic. It’s not one Congresscritter, one vote, but one State, one vote. Each State’s congressional delegation votes on who to cast their State’s vote for. If there is a tie, their State doesn’t vote. 26 States must agree in order to elect a President; if a three-way tie seems unlikely to be broken by Inauguration Day, the duty of electing a Vice-President, who would serve as Acting President until the House reaches a decision, falls to the Senate.

Note that first and foremost, these rules handicap independents, since most of the Congress will be made up of members of the established parties. I assume this would practically eliminate Sanders. The situation for the Republicans is more interesting. Given that a Trump nomination would be to some extent a “hostile takeover” of the GOP, I could easily imagine many Republicans would prefer to elect someone else; maybe they would even split into Cruz and Jeb! factions!

Note that assuming the Republicans control 26 States between them, they could split their votes however many ways they like without any risk of throwing the election to either of the Democrats. How willing they are to do that will depend a lot on who controls the Senate after the elections.

The House is required to choose from among the three highest finishers in the Electoral College.

Ah! Thank you. Ignorance fought. In that case, yes, I assume the Republicans would all or almost all unite behind Trump.