I'm thinking of pulling on the other woman's hair in the bar.
Why would you want to pull on her hair? That is not very nice.
According to your logic, yes. I'm with another woman who was picking on my girl.
Technically pulling someone's hair would be the use of force or violence upon the person of another and, if unlawful it would be considered a battery. Find more constructive ways to communicate your feelings to her.
I'm going to pull on the other woman's hair.
That is just going to get you into a fight with the woman you mess with. You should restrain yourself and not try to fight a woman in the bar.