Just as a matter of law (yeah, I went there), I don't think you can deny any otherwise eligible student a chance to try out for a school team. If she wasn't kicked off the team the year before, the coach shouldn't be allowed to summarily deny her the opportunity to compete. And that is the way it should be, otherwise any coach could exclude anyone for any reason, including many that most of us would find extremely offensive.
Thinking bigger picture: you really should take the AD's advice to heart. Even if she tries out, they gave you the ultimate heads-up that this is not a good situation for your daughter (I'll avoid putting fault on anyone for this post). If she tries out and is cut, how will that help her? The coach does have the right to pick the final roster and talent isn't the only criteria.
EGH...you can't deny them a try out. We saw a HS Girls Soccer coach tell returning Seniors who played varsity the year before that he wouldn't cut them. Soccer is a cut sport. But they wouldn't see much field time. He left it up to them. The 4 he spoke to decided not to tryout/play. They didn't want to put all the work in and never see the field. Right or wrong..he was up front with them and allowed them to make a decision.