At a guys prospective (hopefully some ladies will chime in).
In my opinion I think you took the right approach in telling her about your family and your past and that your mom had a birthmark.
For the record as of right now doctors have not linked birthmarks to be gentic. Meaning that as of right now people with a birthmark can not pass it onto either children. I know several people that have children men and women that do not have a birthmark. I know of one person that has children with a birthmark that has a birthmark herself, but as of right now they still can not prove that she passed it onto them.
As a guy with a birthmark, people have a tendacy to judge me because of my birthmark. If you have already got over that herdale in your relationship I think she should give you another chance. Show her, or tell her that you have cared enough about her that you came to this site to find out and learn more info about her condition.
Hope this helps and things work out for both of you.