I understand that this is unfamiliar and can be challenging for many. At some point, we have to decide what is an acceptable reason to be uncomfortable, and what isn't. Think about it this way: what if it was a lesbian student, and the district said that she had to use a separate locker room? What if the student in question was black, and white students were uncomfortable using the same drinking fountain as the black student? Reasonable people can disagree about what is appropriate, but I, and the ACLU, and the Department of Education, agree that "discomfort" in this case is discrimination.
To get more specific: what is the actual worry here? That your daughter would find out what external genitalia look like? If she goes to a D211 school, she's lucky enough to have sex ed as part of a required health class.
Are you afraid that the transgender student is going to behave inappropriately? Because that's not determined by whether the person is transgender or not-- straight, cis-gender students can behave inappropriately in a shared shower situation, too.
What is your actual concern about having a transgender student showering in the vicinity of other students that share her gender identity?
(FWIW, I grew up in the area, and graduated from Palatine HS, a D211 school.)