Hi
just to weigh in I am an exercise physiologist/S&C coach and have been working with/researching elite dancers for the past 30 years. The personal experience of one dancer is hard to transpose to another. The comments from the schools were very unhelpful and if this was their main issue, you daughter not getting in was probably a blessing in disguise.
Body shapes vary widely in dance and even within genres. Genetics can't be altered and your daughter will be a mix of her parents/relatives body shapes - you can fight this, as historically has been the case within dance, but this just causes serious problems for your daughter later on. If she is prepuberty then it is only afterwards will you have an idea of what her "shape" will be (prepuberty children usually put on weight so they have the energy for puberty).
There is a lot of practitioner wisdom on the benefits of Pilates but under research conditions they don't stack up. The exercises don't actually increase the length of a muscle; they do promote the use of slow twitch fibres as the movements are controlled and with a low load that might be seemed to result in "lean" muscles but are certainly the reason why few ballet dancers (particularly female) can jump.
As others have said hyperextension can lead to muscle imbalance with more loading going through the quads. The development of the posterior chain (back, hamstrings, gluts, calves, etc) could be beneficial - this chain is often weak in dancers.
Cross-training is becoming the norm for dancers now but finding a good knowledgeable trainer is difficult. Swimming is a nice recovery exercise but is not ideal for the development of cardiorespiratory fitness specific to dancers - running is better as long as the technique is good and appropriate shoes are worn. Running is often seen as a no-no but it is actually good as works the internal rotators, the posterior chain and improves jump height (a little) a good stretch afterwards is recommended.
As others have said as a woman development of muscle is very very difficult so resistance training is fine and could be beneficial - there has been some nice research indicating the links with poor muscle strength and increased injury incidence.
Hope this helps
