Hello,
I only have a 16-month old, so I cannot offer advice from a parent's perspective, but I can offer one from the (adult) kid's perspective. When I was 19 I was in a very similar situation to your son. 19-20 is such a hard age. You are an adult in so many ways - your personality is set, you are firm in your convictions and ideals, and you are beyond any parenting like grounding or curfews (even if you live with your parents). At the same time, you are just learning who you are in the big world, not just your family's world, and that is very, very scary. When I was in this place in my life, I started dating a guy I met at college who was all wrong for me. He was controlling, manipulating, all the things you are describing in your son's girlfriend. It caused a major rift between my mom and I, who had always been very close. It took me five years and three break-ups to work him out of my system. It all had to do with me, my self-confidence and my own self-image. There was nothing my parents or my siblings could have done or said to make me change my mind about dating this person, and their saying things against him just made me push them away. I had to come to my own conclusion about how bad he was for me.
When the relationship was finally over my mom never held it against me, and I have been so lucky and grateful to her for that. She said she was just so glad to see me smile again and to have her girl back. As you use the term "adult" in your subject line, you know that at 20 your son is his own person. Even though he is living with you, you can't "parent" him anymore. He is clearly searching for some answers and it will probably take him a while to find them. This will be especially hard while he is living with you. You can set boundaries about what and who you want going on in your own home, but you can't forbid him to see this girl anymore or anything like that. It will just push him back into her arms. It is so great that he is in counseling, but that is a process that takes a long time. Keep your home safe for you and the rest of your family, but just let your son know you respect his decisions as an adult and that you love him. He has to find his own way out of this. When he does, you'll have a much easier time reforging your relationship if he knows you were there for him even when he lost his way.
That being said, your statement "she wants to run us and him" - that you can do something about. Your son is dating her, not the rest of your family. You extended the opportunity to be a part of the family and she has refused. You are now free to gently, but firmly remove yourself and the rest of your family from their relationship. This would probably be a healthy thing. Make your own plans and move forward with them without getting tied up about whether or not they're there. If this girl feeds off controlling others, take away her power to do that over the rest of you. She'll see there's no gain for her there so she'll eventually stop trying.
Good luck