Once the electoral college has voted and it's certified, or Congreff holds a contingent election, there will be a president-elect. Inauguration day stays the same.In my opinion, Trump should also not leave until everyone is satisfied by an election. That is, even if another election is required to bring the necessary transparency, it is Trump's duty to stay. If ever there was a "national security" concern that was ever actually legitimate, this is it.
I propose he stay as long as it takes for legislators on both sides to agree on a national protocol for federal elections, and to implement the protocol with another election that everyone can trust.