Gf mom is mad at me please help

I really like my gf we have been going out for 4 months now.shes 18 and im 17 a few months ago my gf mom saw a picture on facebook on me and my gf and she was sitting on my lap and kissing me. After she saw the picture she said we was not aloud to date or see each other anymore. So since its the summer time and we are out of school and we are still not aloud to see each other I went to her house 2 days ago with my moms car witch I know was stupid on my part. I only went over the for 5 minutes we just messed around but we did not have sex.Yesterday me and my gf were texting about what we did that day that I was over her house. She had left her phone on her bed to go pick up something in her room. Then her mom comes in her room and my gf dives on her bed for her phone then her mom instantly knew something was up and read all the messages. Yesterday was my birthday and her mom knew that. After she read the messages she instantly called my parents. My parents were really peed and yes I know what I did was bad and I take full responsibility for my actions I just want to find out a way to gain my parents trust back and find a way to fix things with my gf and her mom. My gf mom treats my gf like a baby we cant date over a picture she would not even let her see me on my birthday before all of this happen but what really got me is that her mom told my parents what happened on my birthday. I'm a really nice guy I just make really stupid desestions sometimes. Can somebody help me please I really love my gf and want to be with her. I tryed apologizing to her mom before about some stuff in the past and she still thinks we should be friends and not date i need help. My parents dont want me to have contact with any of them period but I just dont like it when I know that someone does not like me I just want to fix the problem I was gona write my gf mom a letter and apologize for my actions and ask if we can meet up and talk face to face but Idk if thats a good idea please help plus my gf mom is takeing away her phone untill she finds a job witch is already hard enoth to do.

Talk to your gift & ash her if she thinks its OK. She might think its not so that's why it's better to talk to her. She knows her mom better than you, you know what I mean?

Gf* Ask*