A bit puzzled by your terminology here. Dual award science is presumably what she would do if you didn't opt for triple. By adding on the extra bit next year, that would effectively become triple science; triple is just one more module of each of the three sciences, on top of the dual award. If this were me, I would clarify that first - because that looks like your easiest way round this to me. Science is compulsory and I can't imagine that means anything other than dual award being offered to all.
Where we live, you can do GCSE music through the county run music centre. There is a cost attached to this but it isn't as high as if you had private lessons. The other thing to consider is grade 5 music theory instead, if she enjoys the theoretical aspects, and keep plodding through the grades on her instrument too. But I agree, I would tackle the school first, clarify exactly what the science options are and then complain if her first choice can't be accommodated.
No, Single Science, equivalent to one GCSE is the compulsory Science subject at my dd's school, Dual Science, equivalent to 2 GCSE's is the extra bit you can add on the next year, whilst Triple Science is an option choice offered alongside all the other non-compulsory subjects such as History, Geography etc.