You didn't mention whether your dd is planning to major in dance or a dance related course of study. If that is the case, then look for the quality of the dance program. What do the studios look like, what courses are offered for all 4 years, who are the faculty members, what are the performance opportunities. Can a dance major have a double major if they want... those sorts of questions.
If your dd wants to dance in college but not major in dance, there are choices too. Some universities have very active dance/ballet companies.
Our dd danced professionally immediately after graduating from vocational training school. How did she get her job? She auditioned (a lot). Not one of those auditioners asked where she trained or where she went to school (vocational, university or otherwise). The only thing that matters, as GTLS alluded to, is the dancing and the current need of the company for a dancer with the skills you show during the audition and also the obvious physical factors.
Our dd is now in college. She attends an Ivy League University. Not one of the questions on the application asked her where she had danced. She used the experience in her essay but dancing is not a requirement of college. The Ivy League schools have a ballet consortium and if the need is there for more ballet dancers, an applicant might have an edge, all other things being equal. Our dd sustained a career ending injury and did not offer to participate in the consortium. Acceptance to these schools happened without her offer to participate.
My point is that dancing in a ballet company and studying dance in a university company are two different worlds, with two different missions. It is difficult, if not impossible to predict which school will be better for a dance career and it is difficult to predict which university may be more interested in the attributes of your dancer. Choose the University based on the academics and that fit the areas of interest that your dk, not on "recognition by ballet companies." Directors really don't care, in our experience.