I am sorry to hear of your daughter's diagnosis. The answers to your questions depend a lot on the grade/level/depth of her melanoma. In early cases melanoma is completely cureable and she would be considered 'cancer-free'.
I don't believe that melanoma is always due to childhood exposure but it is a risk factor that increases your chances. Fair skin and blue eyes are also risk factors along with family history, tanning beds, and increasing age. Please don't blame yourself for her childhood exposure. We know more about these things now than in the past and we all take risks in our lives or we would never drive or fly or live at all.
Take care.
My 23 year old daughter just had a malignant melanoma mole removed from her leg. She has other moles which are now being watched. What are the chances that she will have reoccurring cancerous moles show up in the future? Does she now have a life sentence to cancer or can she be considered "cancer free" now that the malignant mole has been removed? Are these kiinds of moles ALWAYS the result of sun exposure during childhood?