Hi Summer,
I'm not sure how you can see her mom's concerns as warranted, yet also unnecessary. If something is warranted, isn't it also necessary?
Anyways, I like her mom. She's recognizing the emotional needs of her daughter, and also her emotional vulnerabilities, too. She sounds open minded and enlightened. You can work with this, and you can also tolerate it b/c there's a better chance she'll continue to evolve her position as she gets more information about the newness of this current situation, and feels more comfortable with it. Your task is to give that to her, indirectly.
With that in mind, (unless I've got that part there all wrong about her), this might be one of those situations where patience is the best advice. You can ask your g/f what her mom's concerns are, just so you have that info, it's important. Then, you can try to address those concerns not directly with her mom (which could be experienced by her as a challenge no matter how you put it), but to make sure you're saying/doing/behaving in ways to give her the new info she needs to get comfortable with this next step.