Lying to my girlfriend about father's day

My girlfriend made plans for us to go spend father's day with her family. I love my girlfriend, but I can't be around her family for more than 30 minutes. They all are convinced I'm retarded. I have a speech impediment and I'm autistic. I get it. When I open my mouth I sound slow. I'm not extremely smart but I'm not as dumb as they people make me out to be. When her mom found out I had autism, she said in the most condescending tone "Oh bless your heart." I can handle her mom. She is rude to me, but passes it off of nothing because she does it with a smile and as hurtful at it is, I can handle it. Her dad, I can't. He calls me a retard so much her younger cousins thought that was my name. He yelled at me in front of her and her friends because I needed to go to Reasors to pick up some more plastic cups and I told her that but because of my speech impediment I said Weasors. Her dad got in my face and Reasors 4 times. Our entire 3 years together is her family picking on me about my speech impediment and autism. I don't want to deal with them all day. I've talked to my girlfriend about how everyone (mainly her dad) treats me and she defends them because they're her family and just tells me to fix my speech impediment. I know lying is wrong and all that but I told my girlfriend my job wouldn't let me off for Father's day. Truth is I never asked. I didn't want to lie but I also didn't want to fight with her. She loves her family and that's good, but I can't deal with them. I tried.