Glad they came to their senses, Boo - and it shows that you were sensible to appeal.
Spudqueen's absolutely right in saying that you must never let your daughter think she's been naughty, mum22. She hasn't. Many factors are taken into consideration when schools look at applications. Obviously places go to children living in the locality/catchment areas first, because of class sizes and so on, but by all means appeal. The LEA will probably decide in your favour.