As far as I can see you have no contract with her finance company and therefore no obligation to them. You can quite happily tell them to do one.
I would then place it in writing that you intend to pursue her for defamation through the courts, that you have instructed your solicitor to begin proceedings and that she will shortly be hearing from them. Obviously you haven't, but it'll make her back door twitch a bit when she reads it.
I had a similar thing about ten years ago, couple phoned wanting to trade a very tidy Freelander in for a 206 I had taken in part ex. The deal made no sense to me at the time and to be fair I ignored their messages for a few days. They were persistent so I did the deal with them, but thought they would be trouble. The wife was a proper stuck up cow, some sort of trophy wife. They were a nightmare. Within 2 days the penny dropped this wasn't the best move they had made and so the messages began. First they wanted the old car back because she suffered with claustrophobia. I couldn't because I already traded the Freelander out. Then they tore the 206 apart, found the most trivial of faults and plastered reviews everywhere. I threatened them with court and the reviews were removed. They also told me that the 206 had been over-priced and that there was a law against selling over priced cars. She couldn't tell me which law it was but there definitely was a law. She would "accidently" send me text messages meant for her solicitor.
After a month of obscene messages from them at 2 am, refusal to let me have the car back to inspect, I think I refunded them around £500 as a goodwill gesture to shut them up. I made them sign an agreement that it was in lieu of me undertaking any repair work due to our inability to reach agreement and that it was not a price adjustment.
I made them come to me to collect the money and when the wife showed up this time she was rough as rats, no make-up and aged about ten years in a month. Shame.
Going back to her moaning about the drop in the Picanto's value...….Brexit, tell her its all because of Brexit. Probably why its squeaking as well.