Family argument

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How do you handle family argument? I just had an argument with my mom the other day and it was because of my bf. My bf just said something to my elder brother that he will give him a CPU in exchange to his motherboard and video card (but my bf have to check those stuffs if its working fine) but my brother said to return the video card. My bf changed his mind the next day but he doesn't want to tell it to my brother, and he just saying to leave it that way. I insisted to inform my brother because I don't want my bf helping my brother which he doesn't feel good about it and that he thinks that he will not benefit from it. I informed my brother about it and said sorry about what just had happened. Its my bf's fault because he was the one who offered the help and the idea of swapping, my brother just agreed to it. I'm trying to control myself not to hurt anyone's feelings. I said to my bf to return everything and I will just tell my brother that they will no longer continue the swapping idea but my bf will still check the motherboard if its working fine (apparently not). So my brother and I had a little talk and I kept on apologizing. I told my mom about it and she said that my bf is no longer welcome in our house anymore. I said to my mom that it is really my bf's fault but she doesn't need to do it that way. I still feel that I also have the right to decide who should not come into our house since I'm the only one who is working in my family. I said that my bf may have made a mistake today but surely he was not the one who cancelled everything but I am. I also said that my bf helped us in different ways and I don't think it is right to block him from coming in our house because of just one mistake. I do respect my mom but I feel that sometimes they think they're always right. My mom and I are okay now. I don't think I've handled the conflict properly and it became worst. What do you think?