How should i deal with a family fight?

my mom and sister are having a big fight(not physical). they just got back from a trip over the weekend and my sister is finally talking to my mom about showing off. my mom always shows me and my sisters off to other people by talking about our accomplishments extensively. my sisters and mom went to have some interviews at a law school and ended talking to the dean of admissions. so my mom went off talking about all these things my sister has done and how she is so intelligent and she has done so many things. and my sister has, she has done so many things to get involved in her school so its not all lies. but my sisters and i get embarrased when she says all this because it makes us seem errogant and we like to stay modest and subtle. but now my mom and sister are arguing and shouting and my mom is saying shes going to leave tomorow and stay somewhere else but i wont let her and i know she wont because my parents would much rather make sure im ok than fight with each other. but what should i do. is there anything i can do. and i feel like its my fault because i started saying stuff about how my other sister was talking to her boyfriend about how she was embarrased about my mom talking to the dean and making her sound like a member of mensa and some amazing person. and so i told my mom that she was sad and embarrased. then my other sister said that i was right and that she does show us off and we dont like it and so my mom started saying how we should be thankful she says stuff about us. and we are but not when she gives people our life story. its annoying. so what can i do to help cuz i absolutely hate fighting and arguing unless im 100% im right in which case i usually make a bet that im right. but never the less, i think it is a waste of time