In this timeline, the Neo-Zeon War (the first; there was no second, hence the lack of numbering) ended radically differently due to a long chain of events: due to Amuro's interference, Gihren failed to kill Degwin with the colony laser and Degwin basically gave Revil a free hand to deal with Gihren. So Gihren took over A Baoa Qu and launched a coup d' etat. Because of this, Kycilia wasn't at A Baoa Qu and Char consequently couldn't kill her. Because of that, Kycilia made it to Axis and assumed command instead of the Karns. To prevent a succession crisis, Kycilia deliberately remained single, designated Mineva as her official successor and when she found out about Glemy's existence, took great pains to have him raised into someone who's loyal to the dynasty but has no personal ambitions himself, kinda like Dozle.
Except due to being raised as a decent human being, Glemy recognized that there's no point in going down fighting a war and spending the rest of their lives on the run from Federation security, so he overthrew Kycilia in a coup and contacted the Federation to officially request a ceasefire and parlay as Mineva's acting regent. To distance themselves from the Titans' actions, the Federation agreed. Negotiations commenced and in the end, a peace treaty was signed, recognizing Axis as an independent state. In return, Glemy agreed to extradite Kycilia and a number of other individuals for war crimes trials, pay war reparations and clean up the shoal zones left over from the One Year War. As a result of said cleanup, by UC 0100 Axis is in the process of replacing Moussa with a Stanford Torus built around the asteroid's rim from salvaged materials and is a major spacecraft manufacturer; they even built a few improved Salamis Kais for the EFSF as a PR stunt.
Most of the moderate Zeonic resistance members on Earth who were in it for the patriotism rather than the ideology disarmed and emigrated to Axis (which is partly why the Federation allowed Axis independence: to get rid of these elements without having to lift a finger), but there were still a number of radicals left planetside. Knowing that he's related to Gihren, people were skeptical that Glemy would actually resign upon Mineva coming of age as he pledged - but to their surprise, he did just that and left Mineva a constitutional monarchy rather than a dictatorship. Even so, relations between Axis and the Republic of Zeon were initially rather cool, but improved after Mineva, as her first act as Sovereign of Axis, extended diplomatic recognition to the Republic along with a binding legal document where she, as both Sovereign and head of the Zabi family, formally forfeits any and all territorial or economical claims to the entirety of Side 3 and all other domains held currently by the Republic or formerly by the Principality. This latter part naturally draws sighs of relief from Federation citizens, as it means that the Principality of Zeon is finally dead and buried for good and the rot that has been cut out by the One Year War is finally healing; it also prompts the Federation to cautiously take a wait-and-see stance and temporarily suspend the Republic of Zeon's dissolution in UC 0100 to see whether it's actually possible for multiple states to coexist in the Earth Sphere without going at each other's throats after a few years.
Some of the radical diehard elements of the Zeonic resistance still holed up on Earth tried to get Axis' assistance in their struggle but after Axis arrested and extradited a few of them to the Federation, they stopped trying and declared Mineva and Glemy to be Feddie lapdogs and a disgrace to the Zabi name. In response to which Mineva pulled out the steel beneath the silk and reminded the Federation that former Principality citizens do not get implicit Axis citizenship, ergo Axis will not lift a finger to save their asses from execution as terrorists. They fuck with the Federation, the Federation has every right to fuck right back and Axis will stay out of it. And as she's declaring that, Revil has a flashback of Degwin (who has since died of old age while in house arrest) similarly giving him a free hand with Gihren after the assassination attempt by colony laser and wonders whether the daybreak after humanity's nightmare has finally come after all...
Basically, if you consider the Principality of Zeon as Nazi Germany and canon Republic of Zeon as West Germany, in this timeline the Republic is East Germany and Axis is "West Germany with the British royal family".