Hi
I know quite a lot about this subject working in the field....and I am shocked they did not see your daughter that morning, especially when you stated she had a rash - normally at least the nurse would assess this before turning a child away completely. GPs have to offer a suitable alternative to the situation too, so if you felt an evening appointment was unacceptable and you could not walk to the A&E, or afford a taxi, they should have offered to pay for your taxi (which they do in most practices nowadays).
I hope she is okay and it was nothing serious.