I think that depends on a couple of things.
First, how serious is your relationship with your girlfriend? If she is just someone you're dating casually, you should definitely put your mother first! But if she is someone that you are really serious about, who could potentially be a permanent part of your life or atleast for a while, then you might think about things a bit differently.
The thing you really have to decide is what is important to you. Relationships aren't about ranking people in order of importance. If your Mom is consistently being put 'on the back' burner for your girlfriend, or the other way around, then who ever is getting all the 'priority' should understand that both of those people enjoy you.