I hate all forms of faking a tan...
BUT, I am aware that there are different levels of how tan a spray tan you can get, also, it only lasts a few days. So, IF you all are going to let her do it, have her get a light tan, and keep in mind it only lasts for a short time.
I personally don't like that form of payment. Not my style at all! My problem wouldn't exactly be the spray tan itself, but the fact that that is how she is getting "paid". Has the 14 year old wanted a tan? OR, did her mom choose it BECAUSE she's pale? THAT would bother me, and at 14, what girl isn't already in an awkward place? I hope her mom isn't making her feel insecure of her natural self...