I broke up with my girlfriend after she threw my socks in the trash at my mother's home

I bought some socks from a sports store and then I wanted to lend them to my girlfriend so she could see what socks I like and then she could decide which color she liked the most so I could buy a pair of them for myself. I was visiting her and my mum when I did this. I was watching TV with my mum when my girlfriend went to throw away the garbage. She took it to the trash can and was about to throw it when I noticed that she was about to throw the socks out too. I told her that I was about to lend them to her so she could see which color socks she liked the most and then she could show me which one she liked the most so I could buy a pair of them for myself. She told me that she didn't put them in the bag but that they were in the bag when she saw them. I didn't believe her at all but I acted like I did so that she wouldn't get mad and ruin the day. That night we were visiting my mum again and I saw that she was throwing out a cookie wrapper. I asked her if she was sure that she didn't throw anything out with the wrapper, like the terrible liar she is she told me that she didn't. I told her that I was going to look in the trash can if she didn't mind. She told me that I couldn't look in the garbage because she already threw out the wrapper. She kept arguing about it and I told her that I was really going to look in the trash can. She told me to get out of the house and never come back. She started crying when I got up and left. She started shouting at me and asked me why I was so mean to her and why I told her to get out when she didn't do anything wrong. She told me that she loved me so much and that she never betrayed me. I told her that I was leaving. She asked me where I was going and I told her that I was moving back to the town I used to live in and that it would be good because we could finally have some space. She was crying and begging me to stay with her and telling me that she didn't throw out the wrapper and that it was her ex who threw out the wrapper. She told me that she knew that I was upset with her but that was no reason to leave her. I told her that I wasn't upset but that I was just sad and that I needed some time for myself. She kept crying and begging me to stay and told me that she was going to kill herself if I left her. I told her that I was leaving and I left. My mum was begging me to stay as well and told me that they would miss me and that I should just forgive her. I told my mum that I wasn't upset with my girlfriend but that I was just sad and needed some time to myself. My mum told me that it was okay and she told me to call her in the morning so she would know that I'm safe. I told her that I would call her tomorrow and left. Ever since then my girlfriend has been begging me to take her back and to forgive her. She even threatened to tell all our friends and family that I was abusing her and that I told her to kill herself. Ever since then my mum has been calling me and telling me to forgive my girlfriend and to take her back. I don't know what to do. Should I just forgive her and take her back or should I leave her?