i've dived all over the caribbean and my advice for who your daughter should dive with in cozumel is "nobody".
Cozumel is nearly all drift diving over walls and is not appropriate for a new diver, both from a safety standpoint and from a "she may get the crap scared out of her and never dive again" standpoint.
i vehemently disagree. There are many places in cozumel that would be appropriate for a new diver.
your daughter is a brand new diver and does not belong at 90' on her first dives. Even if they promise you "everything will be ok." even if they promise you a private dm.
I don't think that anyone is suggesting that she go down to 90' on her first dives. An private dm at 60' +/- would be a very careful and cautious approach.
my suggestion would be to schedule some nice quiet shallow dives over a hard bottom in curacao or bonaire if you're going there, or make specific arrangements with a dive op on another island for easy dives over a hard bottom.
but, they're not going there.
scubaboard is littered with threads about new divers being taken where they don't belong and being scared witless and/or injured and in some cases killed. Don't let the fact that you'll happen to be in coz be the deciding factor that she should dive there.
littered with threads? Additionally, there are new divers, and then there are new divers. In this case, i think the parent has an idea as to whether his daughter has any aptitude for diving, and how much.
what islands are you going to?
Flots.