Hi,
Your son is old enough to have his own life apart from his original family, your family. If his girfriend does not like you, so be it. You cannot force someone to like you, maybe she sensed that you don't like her too. No matter what it is, don't be in the middle of your son's relationship with her. Leave them alone, they are old enough and she is your son's choice. You don't have to like her too. The most important thing is you need to be polite and be civil when you are around her.
This is not the first case wherein daughter-in-laws and mother-in-laws don't get along. I think it stems from jealousy and the fact that the mother still thinks that her son is still the young boy that she had before and also the mother thinks that the new girlfriend or wife is taking their son away from them. Please change your attitude toward her. Make her feel welcome to your family and make her comfortable. Treat her as if she was your new daughter, not your son's girlfriend. Then possibly you'll have a better relationship with her and your son will be happy too because he does not have to take any sides. But in the end, if he married her, he probably will side with her. Also, when they will have children in the future, you may want to see your grandkids. So it's good to patch up your differences with her. As long as she loves your son and does not cheat on him, let this issue go.
My advice: Be NICE to her.
Take care.