It wasn't accidental. I'd remember that in my counter. They are trying to skin you because they felt like you skinned them in the renegotiation. These are tit for tat people, not fun do do real estate transactions with. It also sounds like they are having a little seller's remorse between the delay in signing and now the use of additional points. If you do deal with them more, I'd do so with no mercy and with every intent of walking away if they don't jump to your tune.
When we bought our house in 2011, the seller was a maniac and got angry and resentful about every single thing in a normal transaction (home inspection, requests for credits for deficiencies and code issues, etc.) We found out later that a) she was crazy, like charged with crimes-type crazy and b) was forced to sell the house in a divorce proceeding brought on by her raging crazy.
She balked at every reasonable thing, forced a bidding war once we'd come to terms more than once. We loved the house so we stayed in it, but it was a nightmare. When we finally had a closing date and inspections, she didn't want to do anything, didn't want to pay for any problems she'd tried to hide, etc., etc. It finally came to a head and I lost my cool completely when I went to use the restroom during an inspection visit and the toilet that she swore she'd fix didn't flush. I told my agent I wanted $2000 for the toilet. He told me I was crazy. I told him I was tired of her games and I'd lose the house over it, but that toilet was going to cost her $2000 if she still wanted our check later that week, and if he wanted his commission he'd better communicate our instructions clearly.
She blinked, and I got a $2000 toilet. But she threw a garage door opener at my head at close. So there's that.