How do you forgive and forget someone who has wronged you?

I thought my best friend - whom I known for 12 years- was a friend until she decided to ignore me a few months ago. I've always been nice to her despite the fact that she is a pessimistic and cynical person. For some unknown reason, she's always angry and often acts as a debbie downer. Last year, I got a huge promotion at work and was transferred to NY for a few months. She acted like she was happy for me but instead, chose to cut me off. I didn't rub it in her face or anything and tried to include her in my life. I know understand that she was not a real friend and although I feel sad and cheated, I want to move, forgive and forget her so I can focus on my happiness and life without this toxic person in it. The part that sucks is that her mom considers me like a daughter and I'm afraid I will have to cut her off too. What should I do? I tried talking to her and calling her but no response so I just want to move on and be happy.