Hi and welcome!
What piece did you read that a genetic mutation occurs after conception? If you could post a link, that would help other patients with their research.
I remember a study once whose premise was that there was a difference in the placenta of babies with vascular birthmarks. It looked a valid argument and I do hear a lot of anecdotal evidence from parents about problems with placenta. But nothing was ever proven.
If your daughter's birthmark is still visible at 13, you might take her to a specialist. Back then, doctors called every vascular birthmark "hemangioma" but that might not be the correct term for what she has. I think she might possibly have some other kind of vascular malformation... hemangiomas do not appear one year after birth and they involute by puberty.
Anyway, post some links if you can and we'll kick some ideas around!