hmmm i know that it was explained... i think it was because aria's mom didn't give the man her real name (because she was a prostitute and all) and once the father went back to his country, he couldn't leave for some reason, so it made it super hard to find her. he might have gotten sick?? i forgot, sorry T-T he's a good man though, he's head over heels in love with the mom and treats her super well :)
SPOILER!!!
Aria's grandfather, Marquess Piast (i don't remember their names very well) told her mother that her father had a hard time meeting her mother before and then they never had a chance to meet again ever until the Crown Prince searched for the Marquess (this is from what I can remember from the novel.) U can read the novel at wuxia.com (▰˘◡˘▰)
This is the novel's link
https://wuxiaworld.site/novel/the-villainess-turns-the-hourglass-novel/chapter-211/
Aria is a granddaughter of Violet, who was married to the royal family and drank holy water (it's like recognition of the royal). After some time she had a fling with a marquis from Croa and gave birth to Aria's father Chloe. Then she was cast away from the empire to Croa. I believe it was the time when her son slept with prostitute Apple (Carin, Aria's mom), after that he never came back as he went to Croa with Violet.
So technically Aria is not of royal blood but the pond with holy water recognizes her as royal and that's why she could have a power to turn back time.
So Aria and Asher are not relatives. The ship goes on (⌒▽⌒)
i'm gonna explain what's gonna happen next, so if you don't want to know how this story eventually ends, stop reading.
so, basically, mielle pushes her father down the stairs and blames it on aria but the ml whisks her away just in time (it turns out he has magic powers too, but instead of going back in time, he can teleport which is why he's always showing up at aria's house and can disappear quite easily). the father lives but is comatose and aria has to prove her innocence.
there's a court trial and aria wins with the help of the father (i believe) who wakes up and points out mielle as the person who pushed him down the stairs. mielle is put on house arrest and aria is painted as this kind, forgiving saint. the king who lady isis is apparently gonna marry is actually friends with the ml and there's this whole scheme to take lady isis down. lady isis is imprisoned and mielle is implicated in her schemes. aria "takes pity" on mielle and lets her become her maid. aria tricks mielle into poisoning and killing her own brother (mielle thought it would be aria) and is sentenced to death.
when aria travels to the country where the king who is rumored to marry lady isis is, she meets her father and his family, who turn out to be nobles with royal blood. it gets revealed that people with royal blood get magic powers when they have a near-death experience or something like that, which explains why aria can turn back time after she dies and the ml can teleport after nearly dying. aria's mom divorces the count, but not after taking all his money, and marries aria's long-lost father who fell in love with aria's mom at first sight and has been searching for her since.
aria and the ml get married and it's a happy ending :)
sorry if it's not completely correct, i read the novel a while ago and this is what i remember. the gist should be the same, though!