All the research I have seen does not point to a familial or genetic predisposition to birthmarks. They're just "one of those things" that a certain percentage of the population have. We have a son with a PWS, and I hadn't even really considered that any subsequent children might have one.
And honestly, if any subsequent children have a PWS that needed to be treated, I wouldn't think twice about doing it. Our son goes for his third treatment next week. Each time, I have to remember that the whole thing is much harder on his Dad and me than it is on him! He doesn't seem to be bothered by it much at all.
That would be a good question for the doctor who is treating your daughter, though.