I am not sure where that mother was coming from in her comments, maybe she was just making conversation or maybe she was frustrated that her daughter had to be a part of your dds skirmish. Either way, it was not the right thing to say. It was rude, judgmental and showed absolutely NO empathy.
It sounds like you are on the right track. Parents who are raising children who are neurotypical have no clue how hard it is to be consistent, patient, and fair when these things happen. We have no control over the reactions of our children. I know that people often gave me the crazy eyes over things my little ones have done. You have a few choices, grow some super thick skin and shrug it off. Develop some lines to toss out when these things happen like. I am trying, it would help if you would say a prayer for us. You could confront that mother and let her know that using names like "mouthy" and "sassy" about your children is unacceptable even if she thinks they are true. Are you planning on being a part of that womans life for long or do you think her children will go to different elementary school from yours?
On the bright side, it does pass and your dc will go on to do great things and amaze all of those naysayers who were certain that you were doing it all wrong! LOL!
Hang in there!
