Dealing with smart aleck women?

I cant stand a smart mouth woman.I think smart mouth and sarcastic people tend to be a bit conceited or more.My girlfreind flips off at the mouth for no reason quite often and thinks its okay.She tells me she didnt get smart with me.So Ill say what she says to me to see how it would make her feel,and lo and behold,she gets the same reaction that I got when she did it to me,offended.And she'll flip it around and make it seem like Im the one that does it.Shes very manipulative.Her daughter acts just like her and she says I dont know where that comes from.She'll notice when someone gets flippant with her and be offended by it but thinks its okay if she does it to me or anybody else.Am I over reacting.I only desire respect in a relationship I offer it to them so why dont they do it to me.I only respond back after enough is enough and after I have told her her mouth is very disrespectful to me.Will somebody help me out?