It's a hard situation your daughter is in. I remember being a teen and getting my heart broken over a similar issue--my younger sister made the dance team and I didn't. Anyways, I actually spoke to the dance teacher myself--my mom didn't swoop down to save me and it never occurred to me that she would. My conversation with the dance teacher did NOT change the results. However hard it is to accept, sometimes we simply aren't skilled enough at something. It's a part of the real world, getting turned down for your dream job that you feel so qualified for, etc. Unfortunately we get turned down and don't always excel at what we want to excel at, or even if we do people don't always recognize it. If you really think the coach should be talked to, I really really recommend having your daughter have that conversation with the coach herself, with you there for support if need be. The coach will admire her and take her seriously if she has the courage to ask him herself what she can do to improve.
So, as difficult as it is, I really recommend letting her fight her own battles herself. Be careful about blaming it on the coaches, even if it may be true, and try to point out other areas in which she has excelled. And really focus on her character--things she can control like how much effort she puts into things, versus the results she achieves (i.e. making the team in this instance). She will feel more secure if she realizes that all you expect of her is best effort.
If you go in to fix everything for her, you may not only be taking away a valuable life lesson for her--we don't always get what we want--but even worse you'll send her the message that you don't think she's capable of handling this. I think swooping in to save her as if she can't handle disappointment will damage her self-esteem more than anything else, especially if it's perpetuated in other areas of life. Be compassionate, loving, empathetic, but let her experience this struggle and express the confidence in her ability to handle this heartache. As a mother, this has to be killing you and I'm so sorry you have to watch your daughter be in this pain. Is there another activity she'd be interested in doing this year instead, preferably not competitive and not at the school?