First of you need to know why they went patchy.
Washing up is a big one. I fill my bath up and use washing up liquid to soak my tan off lol so if someone washes up then it will end up making there hands patchy.
Maybe she used hand cream and it was still on when she was getting sprayed?
How long has she had the tan for?
Has she looked after if?
I would not refund, respray her hands for free, maybe give her 20% off her next treatment. It won't be your fault. But it will keep her coming back, explain how it would have gone wrong and you are sorry she's unhappy and would love to see her again and for her to be happy ect.
X