I want to bring peace and harmony to my girlfriend's parents.
That's honorable and a good intention.
Unfortunately stubborn family member may be a true pain in the ass, not because they have a true power, but because of their grasp on your girlfriend's unconscious mind, so they tap straight into her deep mind to keep her involved in never-ending loops of fight and surrender.
I can just add to all the good replies given here, based on experience, there's most often an emotional link between parents and son/daughter that lasts into maturity if not taken care of. This is what pushes parents to act like their daughter is still their "little children" instead of a grown adult who is going to live her life.
This mindset is the most common cause of problems like you describe.
So, even if you cannot convert leftist possessive parents to a healthy mindset, unfortunately, you could take action to prevent they see their daughter as "their own kid". That should be a normal part of human evolution after the teen age.
With magick, I never attempted this, but probably is Moon or Water magick the best to change their unconscious view on her. You probably know better than me how to do this.
On the more practical side, it would be good finding a way to let them project this idea on someone else, while you act magickally, or simply move to your new home.
Like, they have some young girl between their nephews, or friends or relatives, of which they can temporary take care of, or have an interest in. The unconscious may be easily deceived and if they see their "kid" projected into someone else, they will be less possessive with your girlfriend. I did that (or, better said, my GD did that for me with kindness) with my abusive father, who for a while got obsessed with a cousin of mine, who often came to his home, so he could project his idea of "me" onto "him" for a while and I have been able to establish a firmer existence for me, while his mind was busy. This also happened while Neptune was transiting his Sun, so his will was weaker. Planets may help to perform magick, or this kind of operations, by lowering the target defense.
At the end, if you manage to cause this to happen in their mind, it will be mutual benefit for parents and daughter, because their relationship transforms from child/caregivers to woman/parents.
Not easy to do, anyway, in my opinion.