I really do sympathise with you teta, and can relate to your issue on how to overcome. Not only do some independent schools select from their own prep/other prep girls who have had exposure to club/county level, they are very cliquey so even if outsiders do make it to top squads, it can be made quite uncomfortable by the alpha girls because they would rather their mates make the A teams. I don't think the coaching staff are blind to this, but they do turn a blind eye, as they know these are the children from influential/pushy parents that have red inked as 'do not upset'. And a certain amount of attitude and presence is needed in competitive sport that can shadow the less aggressive sports children, in spite of their potential and past achievements.
I know I am sounding a cynic, but over 2 terms of it has made me a little bitter (and disappointed in my DD's school's handling) that resulted in some really unpleasant behaviour from the favoured girls. So, having put a constructive email together, I received nothing back, except a mark down on her end of term report a few weeks later (after 3 consecutive 'outstanding' report marks). With feedback that she needed to up her eye to hand co-ordination. This actually made me laugh it was so off.
She is, this term playing cricket for her local club in at academy level, knowing (and me acknowledging to school) that if this were to result in her non-slection for rounders squad, then so be it. And she would therefore not be attending any after school training. Because she was good, and would feel more valued amongst her external peers than school peers.
We took a punt because though she loves all sports, especially the contact ones, this one (and rounders) were sports she was intuitively good at. But we were prepared to face the consequences of non-selection due to our stand slight petulance from being fed up. She got selected for A team, strangely enough, even with them knowing out of school cricket was going to come first!
Long rant but your DD sounds like exactly the type of person (for all round sportsmanship) that should be included, and can get overlooked for the wrong reasons if you don't start putting her credits in front of the school. Gently find out why she doesn't want you to say anything. We had lots of work to do on self esteem/confidence as after 6 months these girls had sucked it all out of ours. But she's slowly getting it back now...
Sport, for those that love it is so incredibly important as part of school life, so very good luck in resolving!