I work for a dermatologist. With your family history it would be prudent to have a yearly examination. What you refer to as a precancerous melanoma is probably a "melanoma in-situ" which tends to be more on the surface, however, as with all melanomas if untreated has the potential to go deep into the vascular area and spread. Many doctors will go back and insure clear margins, taking from .5 up to a cm of surrounding tissue even with in-situ's. I would want to follow up with my derm to see what the biopsy results were for the other two moles removed on your back. Don't assume if you haven't heard that they are okay. Today, doctor's are so busy and reports etc. can get filed etc. assuming the patient will come back and the results can be discussed then. I have my own personal horror story about that. Pending your results ask the doctor what if any other follow up tests or treatment is necessary and when they want to see you back. Also my derm is big on applying sun screen and not just when you plan on being in the sun. Sun from a car window etc. can get you. Unfortunately the sun today has damaging rays. Melanoma is not aways found in areas with sun exposure, however, particulary true if you have a familiar history of melanoma. Good luck!