So the concept is that had Arlong attacked two years earlier, Bellemere wouldn't have lost like she did, that she only lost so badly because she was half-starved.
So Bellemere survives, gets Nami and Nojiko out, and trains up to go after Arlong. She ends up on Dawn Island, because I said so, and ends up eventually adopting Ace, Sabo, and Luffy.
This AU hinges heavily on Bellemere being a very promising marine that managed to become an officer while shirking any lessons or trainings that would have seen her get stationed outside of the East Blue.
From what little we've see of her, she definitely had observation haki (she knew Arlong and his pirates were there before they got near her) but she didn't know what it was (she attributed it to their scent, which could have been an insult, but given that she didn't use her observation haki for the duration of the fight indicates that she probably genuinely didn't know). There is a possibility that she had armament haki, in that she struck Arlong, a shark Fishman with a body built to withstand insane amounts of pressure, and brought him to the ground. Again, she doesn't continue to utilize it, so we can assume that she didn't know how, or didn't really understand what she was doing.
I'm also gonna giver her conqueror's haki because i want to.
As a marine, she learned what she deemed would be useful in the East Blue, and had no desire to go anywhere else. The Grand Line was just a strip of backbreaking work, the other seas weren't her stomping grounds, and while she did join the marines, prior to that she was very much a thug (as told by the villagers when they talk about her in the manga). Thugs want to stretch a little, but don't usually actually want to leave what's comfortable to them.
So in this AU, Arlong hits two years earlier, and while she does get her ass kicked due to lack of knowledge and training, she lives to get stronger and come back to finish the job. To be entirely fair, he did try to kill her, but it just didn't take this time.
All of this backstory so that I can show you a set of chapters, super down the line, that I did in the outline for this.
No, Mihawk did not go down on Bellemere, other stuff happened and Perona loves to gossip even if she doesn't really get what actually went on.
Other things of note; misunderstandings on an information gathering level resulting in wanted posters for Gol D. Nojiko, a pirate getting labeled as the face of revolution and the World Government can't fix it in time, Big Mom vs Mom Bellemere, Accidental Adult Child Adoption, throwing a surgically removed uterus at an admiral, "I may not be a good parent, but I'm better than you, and at least I tell my kids I'm sorry", and more adventures following a thug trying her hardest to win at this mom thing and deciding that the best way to do that is to collect as many kids as possible, even if they aren't kids anymore.