The illegitimacy of Trump extends to the whole ticket, because the whole administration was elected together. The election of the President/VP together on a Party Ticket (recognized in the 12th amendment) effectively limits the impeachment of a President to cases of individual misconduct. There is no constitutional means for holding a political party accountable for cheating in an election. Yet that is the situation we are in.
Analysis of why Trump won has to be limited to why Trump carried particular states, but not implying that Trump won because of broad national, cultural trends, because he didn't win.
Is there a constitutional means to change the party holding the White House, especially when the party of the President controls the House and Senate?
In today's circumstances, it would require:
1. The election of a new Speaker of the House, either a Democrat, or a respected centrist, by a coalition of Democrats and dissident Republicans.
2. The simultaneous impeachment of the President and Vice President.