I'm totally confused as to why you keep saying you didn't understand the audition process, and that the information isn't available on the NYMT website.
Here is a screeshot I took literally a minute ago. Its is quite clear that if you are invited to a second stage casting workshop that you will be CONSIDERED for a New Musical workshop. It doesnt say that those at second stage audition are guaranteed a company place.
The social media rumour mill did go in to overdrive somewhat this year about if you were at second stage you were definitely cast in a production. FWIW I personally think calling the second round auditions "casting" workshops isn't helpful and also using the word "workshop" in the context of both audition and project can cause some misunderstanding.
If I ruled the world... or at least had input on the NYMT audition process I would define things with the following terms
Stage 1 Audition (Workshop format)
Stage 2 Recall Audition (Workshop format)
Skills Course (Open Ability)
Skills Course (Invite Only)
New Musical Development Project
Production
I would also encourage you to consider that no-one at any point has said your GD isn't talented. To be called back means this has been recognised, but there are many many talented kids in the process and there can only be one selected to play Winnie Foster (for example).
Many many factors are taken in to consideration, when casting (not just NYMT but any professional role) things like age, is it a GCSE year or A level year for the young person , is the actor a believable fit for a family, how is their dance ability, do they also play a musical instrument, do they have a specialist skill (for example skateboarding which may be relevant when casting something like Flip), do they fit in easily to a team of new people, are they likely to be homesick and experience stress/anxiety, I'm not aiming any of these directly at your DC, just generally sharing some other things that may be considered that often have nothing to do with their MT skills (and some of which are completely outside the YP's control to do anything about)
Look at it this way... there are hundreds of premier league footballers. Not every team wins the title every year. It doesn't detract from the footballers talent in any way and it doesn't mean the game was rigged. Its just we can't all win all the time.
Get me making a sports anaology.