My daughter's school do the same thing, though it's brass and other woodwind. So there's trombone, trumpet, French horn, flute, saxophone, clarinet plus a couple of others. The kids got to choose which instrument they wanted.
What instrument does your daughter play, that has the embouchure conflict? I wonder if they would be up for her playing that as part of the lesson?
They can't "make" you take an instrument - you have to accept responsibility for the instrument by signing for it, so I wouldn't worry about that. The people who run it love music and would want to involve your daughter in a way that works for her, surely? I'd try to talk to the teachers.
They don't teach them to read music with it, but by do-re-mi. I really can't see that the lessons would harm your daughter if she can accommodate it with one of her existing instruments, so you don't have the embouchure problem, which I do understand is an issue, and so will the teachers.
The kids love it, and you sound awfully harsh (but we all do when it's the thing we care about) - some of these kids never get the chance to try instruments any other way - your daughter is lucky to have already. My daughter is loving the trombone, and yes, she'll not take it further, but she has appreciated the chance of doing it (they did various drums last year, which was great for appreciating rhythm).
Anyway, I'd try to talk to the music teacher sooner than later to put your mind at rest.