Don't date another chick to make her jealous. Date another chick because you want to date another chick.
Be respectful, yes.
Do your best not supplicate. All kidding aside, when you start doing that and giving in is when a woman will walk over you. Fact is, most women want a man to be just that - a man. They like to be challenged. You challenging them exhibits strength. They don't like weakness. They like strength and the feeling of being protected.
Having that said, I don't know enough of the background story to give a truly adequate response.