Absent severe butterflies, TR would beat Wilson in 1912, Being that he came to office initially due to Garfield's assassination, he could use that fact to "finesse" the no 3rd term issue....as I recall it was not much of an issue OTL.
IMHO the biggest result of TR getting elected is the US does not wait until April, 1917 to get in the war...and "preparedness" starts by late 1914 so when the US enters (probably not until 1915 or early 1916) the Army has plans to induct and train men, more "Plattsburg/OCS" trainees ready, adequate production (or at least decent) of rifles, machine guns etc.
While this will probably end the war earlier, the net result will be many more US casualties which will have some important social/political butterflies...."isolationism" could very come sooner, stay longer, and be stronger...