Okay thanks for the additional information. This mother obviously has some severe control issues going on, and due to this is acting not in her daughter's best interest. Obviously it's not in good judgment to invite abusive exes over to their house. Her mother is really invading her boundaries as well.
Rather than trying to influence the mother by meeting her, etc. I would advise you to encourage your girlfriend to gain more independence from her parents/mother. Also, with the divorce going on, it's likely her mom is going to become even more controlling. Your girlfriend needs to move out on her own and start to be more financially independent as soon as she can. In the meantime, she simply needs to set boundaries with her mom and tell her to not set her up anymore, etc. That if she continues to do such, that she will not be there for the dinner etc. meaning there will be a consequence to the behavior. I would stop trying to meet her mom and again focus more on your relationship with this young woman and be supportive about how difficult this is for her.
I would really suggest that your girlfriend get some counseling about how to maintain boundaries with her mother, as this could be a lifelong struggle otherwise. This issue runs deep and obviously did not begin with her dating you.
Again, trying to control the mother will backfire, so stating a boundary and then following through with a consequence if/when that boundary is violated is the best approach. She needs to show her mother rather than tell her. Please click ACCEPT button so I'm credited for my help today. Feel free to continue the discussion with me even after accepting. Thank you!