If there is any type of bullying going on at school, time to get the principal involved! It is not to be tolerated at all especially at school! If she is a bully to your daughter, then do not allow your daughter to play with her and DO confront her mother. I mean you don't have to be nasty, but you can and should approach her that her daughter has been causing a lot of distress and heartache to your child and it is unacceptable, period. If she is leaving young children at home alone then call social services.
I wouldn't worry about the tape recorder as much as I would be fierce in standing up for your daughter! She needs to learn that it is NEVER okay for someone to be cruel.
We as parents cannot fix every bump with friendships for our children however we can give them the tools to not allow to being pushed around, encourage only being around people that make us feel good inside.
I would tell the mom that kids learn what they know and it is never going to be okay for your daughter to think being mean is okay. She may not care but you do!
Go to the school and confront that woman. If your daughter sees you allowing it she will get mixed signals it is okay. It would be nice if our neighbors were all perfect, however obviously that isn't the case. You may have to live next to her but that doesn't excuse her children being out of control and her not doing anything about it!