Is my girlfriend's girl friend hitting on me?

[barclay76]

My girlfriend has known this girl since she was little. They grew up in the same neighborhood together and both she and her still live in their parents homes. My GF's parents have passed away and she lives with her brothers, sister in law, and nieces. Her friend lives with her brother, sister in law, mother and father. We are all in our forties.
My girlfriend has accused this girl of flirting with her ex husband in the past. They all went on a family trip to Maine and this girl flirted with my GF's ex husband. She called her out on the flirting but they have still remained friends.
Because of the friendship, this girl is invited to my GF's house for parties. Last weekend, as I went to great her by giving her a hug and a kiss, she landed a kiss on my lips before I could lean over to the side and kiss her on the cheek. She has done this before.
My intention was to move to her right side and kiss her on the cheek. Instead she also moved in the same direction and landed a kiss right on my mouth.
My reaction was a bit surprised and shocked. But she just smiled at me and sort of laughed. She did this right in front of my GF.
In both instances, my GF has been in the room when it happened and she barely noticed it.
This girl is pretty. However, she is my GF's friend and I am in a relationship. Even if we were to break up, it would be too weird to date her.
My GF has told me some things about this girl. For years she was sexually obsessed with a Catholic priest. He later left the priesthood to be with another woman and it broke her heart. Later she decided to "switch teams" and began dating women. She has gone back to men, but for some reason, none of her current boyfriends are American.
My GF tells me that even now she is still obsessed with the priest and has night time fantasies about making love with "Father Thornbirds."
When this kissing stuff happens, I just act cool, not upset but not encouraging either. The last time it happened she clenched on to my hands tightly after she kissed me smiling at me. She reminds me of Glenn Close in "Fatal Attraction."
Anyway, if you are too young to remember "The Thornbirds" and "Fatal Attraction," I apologize. But I think you get the idea.
One of my gym buddies said
"Why don't you friend her on Facebook and see if she wants to hook up? I'm sure she won't tell your GF."
My mother tells me to stay away from her but don't tell my GF about what she's doing.
My girlfriend says that I am shy and she wants me to hug and kiss all of her female friends. Once I didn't hug or kiss one of her friends and the girl said "He must think I'm fat." Women, honest to God.