budgiegirl "If everyone felt the same as the OP, there would be no choir at all at the evening performance."
If all the children did not want to be in the choir maybe it would be best not to have one. But the reality is there will probably be some kids who want to be in the choir and that is great.
"I accept there may be occasions when it's just not possible, but this isn't one of them."
Why is this not one of them? That is a genuine question, I am not being goady! 
"... bigger parts will come when the child is in year 5 and 6, and I would hope that younger children will support her then by turning up for the evening performances."
Why does the play or whatever require children from three years? It doesn't require all these kids so why have some there who clearly do not want to be there and whose parents cannot make it work logistically.
We have supported everything our dd did at school, but I don't resent other parents who do not, for whatever reason, because I see this aspect of it as voluntary.
If I were the OP, and my child wanted to be in it, I would see if a kind friend could take her there and back, e.g. another parents. And I would offer the same when I could.
But it is a bit different if child really is not keen to do it.
Also budgiegirl (not picking on you it is just you are saying things I either agree or disagree with!)
"While I agree with this, it isn't really the same thing here. It's fine to allow a child to quit a club they have tried and don't like (although I know from bitter experience it's better to say "finish this term and then see how you feel")
But in this case, it's a one off."
Yes, and I agree with you, it is different.
BUT just because "She doesn't have to do it again after this performance." I still do not think "She'd be letting others down if she didn't go." She is not letting others down. And re "Not everyone can have a starring role, although her turn will probably come. Being in a supporting role is still important to the overall production." We have no idea if her turn will come or if she would want it to.
So, no, IMHO, she is not letting people down. Her mum has to make a choice between taking two very young children to an evening performance or not taking her dd. Plus the dd does not want to do it.
If the dd had enthusiastically signed up for a role and then could not be arsed, that would be different and I would agree she was letting people down, and most of all had taken a role another could have had, but even then - there should be an 'understudy' waiting in the wings, literally, who would be only too happy to go on!
IMHO it is OK to sign kids up for this type of thing (as a teacher, or a parent) but it is not OK to be upset when they make their feelings known and do not want to do something like this. It is not the same as refusing to work or co-operate in class.
For some quite shy kids it is a big deal and although some may find they like it, when forced into it, others may not! Some may be put off this stuff for life by being forced into it, IMHO.