Charlie, you have to understand that there are women who will flirt with you just because you are with another woman.  The fact that you are with someone else possibly makes them feel safe flirting with you.  It also boosts their self esteem to see a man with a lovely woman who suddenly shows interest in them. 

You have no hope with this woman so forget it.  Just accept it and stay with the woman you love.  Trust me, the grass is not greener on the other side of the fence.