TR vs. Wilson Rematch, 1920

[🐒Gods of Prosperity🔱🐲💸]

At the Democratic convention, Thomas Marshall declines renomination for VP, and Gov. Cox of Ohio is selected in his place.  Wilson campaigns on joining the League and rebuilding after the war. Wilson's approvals are low, with a sour economy and a nation wanting to turn towards home. Roosevelt remains popular, and the conservatives in his party are generally willing to back him once he presents Harding as his preferred choice for running mate. Some see both major party candidates as too interested in foreign adventure, which helps the minor third party candidates (esp. Christensen) - but not enough and not where Wilson would need it to win any states outside the South, and the result is a 2:1 ratio in the popular vote in favor of TR.

Theodore Roosevelt (R-NY)/ Warren Harding (R-OH)  60.8% 417
Woodrow Wilson (D-NJ)/ James Cox (D-OH)              31.1% 114
Eugene Debs (S-IN)/ Seymour Stedman (S-IL)           3.4%
Parley Christensen (FL-IL)/ Max Hayes (FL-OH)           2.5%     
others                                                                      2.2%

[🐒Gods of Prosperity🔱🐲💸]

A dead raccoon would beat Wilson in 1920

Pretty much, although the lack of whisper campaigns about his wife running the show post-stroke (stroke being butterflied) might allow him to at least maintain a core of supporters within his own party.

What would be TR's position on the League of Nations?

TR lived long enough that he had a position on the League as the proposals were taking shape. He had proposed an international peacemaking league several years earlier, so he was a fan of it in the abstract, but he was an ardent opponent of what he was seeing.  The League united both hawks and doves in the Republican party in opposition: hawks because it might restrict America from acting in what it saw as it's national interest and imperil the Monroe Doctrine, and doves because it could force America to fight an unwanted war if the League called for it. Also it didn't hurt that it was being supported by a Democratic President and opposing it happened to be a political winner.

It's funny how people tend to look back at who opposed the League and automatically assume they must have been "isolationists" (ex. Henry Cabot Lodge, who was one of the greatest proponents of imperialism the Senate has ever seen).