She definitely sounds like she's got mental health issues. Her obsessive and unreasonable behaviour reminds me of my own mother during one of her psychotic breaks/nervous breakdowns (she's had three). She'd be able to function 'normally', but would be utterly, utterly unhinged towards certain people.
With the third one, my dad couldn't bring himself to have her sectioned again, and tried to ride it out. She ended up harassing one of his employees, as she'd convinced herself that he was trying to steal the family business and our house - abusive phonecalls, banging on their door and driving past/sitting outside their house, etc... then she'd go into work the next day and act as if nothing had happened. My dad stuck his head in the sand a bit - he'd try to talk to her, she'd start screaming at him, he'd leave the house hoping that she'd calm down. She'd make more phone calls instead - the one time I was left to deal with the police, because she refused to talk to them. :(
She eventually got slightly better - her behaviour hasn't been as extreme, but she still suffers from mh issues, which causes problems with my husband and my brother's wife. My brother and I have grown up with it, so we tend to get really annoyed if she does something offensive, but shrug it off fairly quickly as 'that's just what she's like'. Our spouses are understandably less understanding!
But yes, OP, your MIL sounds like she's gone from garden variety manipulative and demanding to full on mentally ill (especially when trying to justify to the neighbour that being locked out of your house was unfair).