Hi, I'd like to help you with your question.
I can understand your anxiety over this situation. You sounds like you are saying that you are fearful that your girlfriend is like her mother or will become like her mother.
While it is easy to think that your girlfriend may become like her mother, if it was going to happen, it would have by now. When someone grows up with a parent who is abusive and acts out like her mother did, the child can react in many ways to the abuse when they grow up. Sometimes the child will model the parent's behavior and become like them. Most of the time, you will see this manifest itself by the 20's, sometimes even in the teens. Usually never as late as middle age.
Other abused children cannot wait to get away from the abusive parent and they usually make an effort to act the opposite of the abusive parent. They will even go out of their way to be sure they are nothing like the parent. That doesn't mean they don't have problems stemming from the abuse they suffered, they just deal with the situation differently.
Most adult children of abusive parents fall somewhere in between. They develop issues related to the abuse, such as your girlfriend's anxiety about her mother, but they don't necessarily act like the parent.
If your relationship continues with your girlfriend and you become closer, you may want to suggest she sees a therapist for her anxiety, especially if it is affecting her daily life. A traumatic upbringing such as hers can cause distress, even when the person is no longer around the parent. Therapy could help her overcome her anxiety and help her deal with any contact with her mother.
I hope this has helped you,