With regard to authorised absence, attendance at an interview (so for dance read audition) should be authorised with the code J - page 19 of this document might be useful to refer to in any dealings:
Incidentally, codes P and F might help those who struggle to get time off for summe schools - the get out clause is 'someone/an organisation approved by the school' but I think it would be difficult to not approve the Royal Ballet Schhol for example!
But to defend schools, attendance is a VERY significant factor in inspection judgements especially in the current policitcal climate, with a focus on safeguarding children and 'children missing education' being something that could send even the very best of schools (however that's is judged) into a requires improvement or special measures category.
But to reiterate, yes you are most definitely entitled to an authorised absence to attend interviews/auditions at other educational establishments and I am sure the school would rather give you an authorised absence for those occasions than an unauthorised one! Good luck!