When Dubya is reelected in '04 he becomes the first president reelected since Nixon '76 and the first to actually complete a second term since Reagan.
I think Trump may be a member of the Reform Party while losing reelection in 2000. There would be plenty of conspiracies around him and how he was forced out by the Bush family and the neocons. When Trump 2000 voters enter or reenter the GOP it spells chaos for the party, which is how Clinton and Obama get two terms each. Former President Trump tried many times to run for a second term after losing in 2000 but due to legal woes wasn't able to mount a campaign until 2020, when he finally lost for good.
As for Jimmy Carter, he chooses not to run for a second term for some personal reason or something. First President to intentionally serve a single full term since Rutherford Hayes.
Perhaps he makes a one term pledge as part of a platform underlining him not being a "Washington" type figure.