What if teddy Roosevelt decides "screw it, I can get elected again"
would Roosevelt running a second time result in his own victory, and would it end the possibilty of Wilson in the next election?
This has been covered elsewhere, but for the heck of it, here's my take on it as an ardent admirer of TR: assuming TR could assuage the rising conservative wing of the party and dissuade Taft from running again while keeping peace, he could secure the 1912 nomination. Chances are he'd wind up with someone agreeable to both wings as a running mate (e.g., Missouri governor Herbert Hadley).
I have no doubts whatever that TR would dismantle Wilson rather neatly in the 1912 campaign, winning another term in his own right. Moreover, due to the enormous prestige and good will TR enjoyed in the chancelleries of Europe, I could see him offering his services as mediator/negotiator of what I'll call the Austro-Serbian crisis in the wake fo the assassination of Franz Ferdinand at Sarajevo in 1914. After all, with his experience in mediating an end to the Russo-Japanese war, he could carry it off, especially with the backing of both Germany and Great Britain. Thus, a general war in Europe in 1914 would be headed off--perhaps entirely.
That in turn would ensure TR another Nobel Peace Prize, likely in 1915. Between a world at peace and a booming economy, another term would essentially be his for the asking in the 1916 election. I can't see Wilson trying again since he would have been astute enough to know it was a losing battle going in; rather, most of the Democrats' heavy hitters would probably have preferred to sit out rather than risk certain defeat. My sense is that they'd turn reluctantly to William Jennings Bryan, since his ego wouldn't acknowledge the possibility of defeat, evidence to the contrary.
The 1916 election would have been a landslide of epic proportions, giving TR a filibuster-proof Senate and an overwhelming majority in the House. That in turn means enacting many of his pet programs (e.g., legislation of the 8 hour day, an anti-lynching bill with real teeth). Also, TR would keep his health reasonably intact, given no expeditions to South America during these years.
I doubt he'd try for yet another term in 1920; instead, he'd have probably mended fences with Charles Evans Hughes sufficiently that the two could work together amiably enough and such that Hughes would be the logical heir apparent. Thus, we're looking at an ascendancy of progressive Republican politics in the 1920s rather than the more conservative brand we saw in OTL.