Welcome to the forum coolboz2009!
I think it would greatly help anyone wishing to give you advice if you shared with us more information. Your age would greatly help. Relationships can be complicated while you're still a minor, and I would hate to give you advice that wouldn't be well accepted by parents.
You shouldn't have to convince a lady to stay. If she is uncomfortable with your parental situation, you're only solution is to reconcile your girlfriend with your mother, or let her go. She should not have to feel threatened and actually afraid of your mother harming her.
