Her grandmother is Tethys, the titaness of the sea. Ladies and gentleman, not only are the Titans, who both in cannon and in mythology are trapped in Tartarus and cannot escape, having demi-titan kids, but the gods don't bat an eye. Worse, she snares Apollo into loving her.
Annabeth is very OOC, becoming a touchy-feely emotional girl (if she gives a reaction at all) who acts more like a daughter of Aphrodite then Athena. At one point she becomes disgusted at the idea of killing somebody (Percy, due to being the child of Kronos, is to be killed if she acts up), despite the fact canon!Annabeth has been trained all her life to kill monsters like replacement!Percy, and in the final battle kills rebel demigods without hesitation.
Grover is pushed to the side as "the goat who freaks out, but we don't really hear about even when he is freaking out." As such, he is fairly OOC, but not near as bad as Annabeth.
Then there's Apollo... This lovestruck loon picks up not only the luv bug, but the idiot ball, even forgetting the fact that he is an almighty god of the sun and could teleport out of a bad situation. Yeah. However, mission wise, he seems to have part of his canon self still inside him, as he gives these gems:
"She was petite and delicate looking, long brown lashes framed beautiful golden-colored eyes and—
Whoa—Apollo stopped himself before he can go further. What was he doing checking a twelve year old girl out?"
and:
"'I'll talk to them about it, they will listen to me." Apollo said firmly, in a rare moment of seriousness Percy looked genuinely surprised that he would do that for her; he didn't fault her. He himself was confused as to why he even volunteered for someone he didn't know except in his dreams."
Still, up to the person who does the mission, if they think it is bad enough to do a mission. Mechanically, the fic is bad, but not atrocious. However, for the amount of cannon it brutally murders, I believe it is bad enough under the Canon Protection Initiative to be itself brutally murdered.