Needing to breakup with my girlfriend?

I have been with my girlfriend for the past 6 months and everything has been going good and well although her brothers girlfriend is very jealous of our realtionship and tries to dictate how we operate as a couple. Although I am older then her and her partner (gf's brother) she continues to speak to me as a child and tells my girlfriend we are not allowed to hold hands or cuddle when she is present. She even verbally abused me and my girlfriend as we were late returning home from a walk together!!! She is a total backstabber and even run downs my girlfriends mother... I moved into my girlfriends place for a short period (2 mths) and the sister in law made everything for me totally crap... me and my girlfriend would be sitting together on the laptop and quietly whisper about what ever we were looking at and the sister in law have had enough and want to end my realtionship with my girlfriend but wish to remain on good notes and still be friends.... I am her first serious boyfriend I just dont know how to end it?? Help please.