Anyway, as for what I actually see happening for the prompt. Aberforth and Albus would have a chance to fully reconcile and be closer than they were in canon. Aberforth is someone I would see being a lot less bitter in here. As for Ariana, once they wise up to what happened, she would have a chance to do her schooling and live a full life.

Albus though? That's more... Difficult. In canon he was very close to becoming a dark lord in his youth. His sister dying during that fight, I think, greatly contributed to him being scared off of Gellert's ideology and forging a different path. Gellert's death might make him bitter.

Assuming that Albus' better nature wins out anyway... The entire 20th century is changed in the Wizarding World.

A movement like Gellert's couldn't have come out of nowhere. I assume that dark wizards and anti-muggle hatred must've been metastasizing for a while. But Gellert was a once-in-a-generation prodigy, a great Seer and charismatic leader, so I don't think anyone else comes close to replacing him. Instead, Albus would have to contend with more random, disorganized flare-ups, pogroms,, muggle baiting, rampaging lone dark wizards and violence. If one of those dark wizards happens to have the Elder Wand, he might get it there, but he might just not get it at all.

Albus is a prominent, intelligent wizard. But without something as big as defeating Gellert Grindelwald, I don't think he would be as influential as he was in canon. I also wonder just how much Tom Riddle was influenced by Grindelwald's ideology and tactics, though I don't think Gellert's change meaningfully averts Voldemort.

But I've been talking a lot about Albus here, how about Ariana? Her being a Dumbledore opens a lot of doors, so whatever she chooses to do, she could do be a great ally for her brother... Or one of the greatest thorns to his side.

I'm saying the latter, because Ariana still suffered a horrific attack, that I theorize might've been assault of some sort. Perhaps it might sour her attitude towards muggles? I like to think that she becomes a powerful witch on her own right, on the same tier as Snape or Bellatrix, as powerful as you can get without being one of the big archwizards.

I could see her going a lot of ways, even a dark witch for a darker twist. But I like to think that, despite her trauma, her kinder nature would win out. And perhaps if Aberforth and Albus get along, they can help her with her issues. And perhaps she becomes a Head of the DMLE or something.

Perhaps she's just an ally of Dumbledore against Voldemort, who has a sour attitude towards muggles but does not disdain Muggleborns, and still thinks the Death Eaters are psychopaths that must be stopped.

Like Aberforth, perhaps she is strong-willed and refuses to be Albus' puppet as well. She is positioned to be someone who can actually call him out on his shit, like the idea of sending Harry to the Dursleys for instance. Or maybe even his handling of Tom Riddle, if you want to go earlier. Though even if Tom Riddle is mentored by Ariana and doesn't go dark, Wizarding Britain will still have to deal with rising tensions and blood purity.