For the past five years or so my neighbour has never failed to make a sarcastic remark to my DD every time she sees her. DD is 14 now and a couple of hours ago was outside saying goodbye to two friends. They were standing on the pavement near a shrub just chatting when she comes out of her house and says 'oh yes, fascinating shrub isn't it?' In winter when DD and friend were outside building a snowman she came outside just to say 'Haven't you got anything better to do with your time?' She has deliberately walked into DD in the street before now, shouldering her out of the way, and generally plagues her with what I guess you'd call low-level bullying.
When DD was nine neighbour said to me 'We could probably get on alright if it wasn't for her. I asked what DD had done to upset her and she said she 'looked at her funny'. I was very 
and from then on just thought ignoring her was the best policy.
I have tried to give this woman a VERY wide berth since about two years ago when I had a visit from the police one evening. They said she'd accused me of criminal damage. She'd told them I'd torn down her fence, which had actually blown down in the wind several months before. I had a broken arm at the time and couldn't have pulled up a bloody dandelion at the time. The police weren't interested in anything I said, but told me to report to the custody centre a few weeks later to be arrested. I was horrified, but the police basically said it was standard procedure (arrest by appointment 3 weeks after their visit...). I wasn't charged and in a five minute interview the police decided there was no case to answer. I was pretty peed off because not only was there no evidence I'd done anything, there was no evidence of any crime. I had gone through all that anxiety and indignity just because of neighbour's malice.
About three months later she called the police again. She told the police DD and a friend had been throwing stones over her six feet high fence at her, which was a total lie (I was there at the time with another neighbour). I told the police I was surprised to see them at my door after her previous false allegation and they went away, saying they weren't planning to take any action against us. FFS! Then I got a letter suggesting mediation. I did meet the mediators but explained that I'd find it difficult to talk to her face to face as she'd told a shocking lie about me that had resulted in my arrest, so I'd struggle to come to any agreement with someone who was apparently comfortable about telling lies that had such huge repercussions. Also, I felt that agreeing to meet to discuss something that had never happened would give weight to her accusations.
Since then she has kept up this campaign of sarcasm against DD and her friends, always when I'm not around, of course. What bothers me is that she goes out of her way to do so, coming out of her house specially to 'have a go'.
The most baffling thing is she has a DD who is only a couple of years younger than my own. She drags her out of the house with her to witness her display of aggression to my DD. I don't get why - as she has a child herself - she can't see how uncomfortable her behaviour makes my DD.
Has anyone got any suggestions for handling this? She is a really nasty piece of work and obviously has no qualms about either her behaviour, or even about lying to the police.
I did actually go outside this evening and tell her it wasn't mandatory to make a sarcastic comment every time she saw my DD and that it was bullying and she just said 'Oh yeah, well you'd know all about that' and smirked at me.