Since your girlfriend feels that your mother is competing with her for you, you can tell her that the best way to win that kind of competition is not to compete. 😉 If your girlfriend considers herself above competing with your mother for your attention, she will have won hands down. In addition, it would be wonderful if she could allow for your mother’s insecurity that fuels her need to compete with your girlfriend for you, to be [i]quirky and eccentric[/i] rather than threatening and insulting.
If you speak to your mother and ask her to stop her behavior, your girlfriend will have lost, and you will have created a bigger issue than what now exists, so don’t do that. The best behavior for you to employ is to ignore it, too. In fact, next time your mother gushes about you in front of your girlfriend, you can diffuse the situation by kissing your mom on the top of the head, and then grabbing your girlfriend around the waist and kissing her on the lips, and telling them both how lucky you are to have 2 such wonderful women in your life, and that you’re clearly spoiled with love.
I hope that helps — let me know how things go.