This is bizarree.
You complain about her splurging information over your family website...and then you splurge your business over one of the busiest forums in the country in such a way as to render her completely identifiable. Twice.
You are angry with her for contacting your father....although you say you feel sorry for her.
Your dad is a lovely man...but he considers his child a nuisance. And wears dark glasses (??)
This woman is being treated appallingly by you and your family. None of this is her fault. Two people brought her into this world and she has every right to seek out one or both of those people to answer any questions she might have about herself. You have no right to dictate to her how she should feel, or whether those questions are valid.
I have a half-brother who I did not know about until I was 16 - he is 10 years older than me. He was adopted by his mother's family after she died and my father abandoned him. My father kept this a secret for many years and it was one of the biggest issues in the complete break-down in our relationship - that damage is only just being tentatively repaired now, nearly 20 years down the line.
Blood ties are a strange thing. There is a very big drive in many of us to know exactly where we came from. Many people are driven to forge links to distant relatives through researching their family trees. I knew very little about my father's family until a few years ago and I worked very hard to make contact with some of them. I would be very angry if someone had prevented this from happening.
You have no right to criticise this woman for following this basic urge to know where she came from. If your father chooses to deny her that, then that is something he will have to come to terms with, but if you get in the way, or encourage him in his denial of her for your own reasons, then you are doing something very, very wrong.