Hi and welcome!
I don't know for sure, but I think one of the reasons that no one can give you a quote on how much treatment will cost is that there are too many factors to consider. Some birthmarks seem stubborn and take more treatments. Some birthmarks are misdiagnosed. The type of laser used would make a difference.
Your best bet is to schedule a consultation and see a physician in person. If you need help with your insurance company, try writing to Basia, our insurance expert via http://birthmark.org/experts.php