Biden is not the VP elect. He's the Vice President. He became that back in January. So if Obama is found to be Constitutionally ineligible then he's removed from office and Biden becomes President, per the 25th Amendment.
There would be no "do-over election", because the XXth applies without requiring another election.
The 20th Amendment no longer applies because the winner of the November election was qualified by receiving more than 267 electoral votes. At this point it is the 25th Amendment that covers presidential succession.
But none of that will happen, because the USSC will not allow the case to be heard.
Yeah there's that whole darned standing issue, isn't there?
Please quote the relevant portion of the XXVth that gives the Court the power to remove a president.
You’re still missing it. If the Court decides that Obama failed to qualify, it would transport its through time to the moment just before the Senate counted the Electoral Votes, and declare that AT THAT MOMENT the person who was President elect AT THAT MOMENT had failed to qualify. Then, from THAT MOMENT the Vice President elect would become the Acting President until a President shall have qualified.
However, there is no provision for anyone to qualify under those circumstances, so Biden would be Acting President until the next regularly scheduled election.