Your mole is close to melanoma, but didn't actually get there. Your children should be examined to see whether they have any other risk factors, such as large numbers of moles or many irregular ones. Most melanoma is no familial. A visit with a dermatologist should tell them whether they need especially close surveillance or not. They're grown-ups, so in the end they will need to be responsible for themselves, but that's true of all aspects of child-rearing...
Best.
Dr. Rockoff