This isn't really an advice forum, but since you're asking for advice...
I don't believe that there is any objective right/wrong when it comes to nudity, so it is entirely up to you and your daughter to decide what is right for you. Some families would see any naked appearance on stage as the work of the devil to be avoided at all costs. Other families are accustomed to nudity at home and would think nothing of a naked (or near-naked) stage role.
The director has fairly explicitly stated that he wants to make money off of your daughter's body. If she doesn't like that she has a right to say so, and you might be able to find a clause in some agreement somewhere that prohibits that sort of thing - but of course the director always has the option to find someone else for the part, which would leave your daughter out of a role (but maybe feeling better about herself). On the other hand, if she is OK doing it, she might be able to negotiate some extra pay (i.e. tell the director that wearing sheer underwear makes her a bit uncomfortable, and since the move is designed to bring in money for the company she ought to see some of that money).
As for your concern about seeing your daughter naked, get over it already. Although many churches will disagree, there is nothing morally wrong with seeing another person naked in a non-sexual situation, family member or not. Unless you find yourself having sexual urges, there is nothing to worry about.
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