I do like the idea of exploring other perspectives of the myths like what MinoHotel did to Asterion and i just wanted to give certain pointers.
*What caused her to want Asterion sent away : It's a complicated question i guess you could say she feared him alongside King Minos, or jealousy of him being blessed by an Olymian -Poseidon- upon birth or even jealous of the attention he was getting since he was basicly helping and tending to every ritual related to Zeus, Hestia and Poseidon, or maybe she had other reasons.
*Why was she abandoned by Theseus : I am not fully versed in Theseus myths but from playing the game MinoHotel we know that he was one of Athena's favourite heros (aka as her personnal anti posidon hunting hounds) and Athena had this obssession with ereasing all that relates to Poseidon from the face of the earth. So Theseus's betrayel isn't that unjustified since he used her to kill the Asterion and then left on the island to die to erease the Cretein lineage as per Athena's orders.
*Did she really marry Dionysus : The awnser is yes, mostly. I assume that you read Lord Dionysus's vote if not i highly recommend it, in the vote he proudly stated that Asterion is his brothe in law and since he and saved Ariadne i am 99% sure that he married Ariadne. A counter argument is that in one of the scenes when the topic of incest between the Olympian gods was brought up between the MC and Asterion, Asterion said that Gods would rather chose a relative as a partner than go through the pain of losing their mortal lover so this could be a reason why in the myths Ariadne was said to marry Dionysus but in reality that did not happen.
Personnaly speaking i don't think that Ariadne deserves a redemption Arc and same goes for King Minos because their actions were the cause of Asterion's exile and torture and she even guided Theseus to kill Asterion.
By reading your post i had the impression that you might be going full bara route and im curious about how you will introduce her.
And on the topic of her being a minotaure, in a recent discussion about Oscar's origins with a member of the community we talked about the possibility that maybe her descendents could give birth to a minotaure as a recessif gene and that makes sense in a way, but her being a minotaure that is a bold idea and i would love to see how you would do it.
And the thing that caught my attention the most is "clutching onto the skull of her bovine brother" , does this mean Asterion gets his mortality back ? did she perhaps take his place in the torture and became a minotaure that way (this is a fitting redemption in my opinion) ? How does the resort connect to the Hotel ? Is the resort owner one of the MinoHotel Mc's descendant ?
I had more comments but it would turn this into a Lore discussion
I loved your idea and i would like to see more.