Unfortunately there are just a lot of people in the world like this: My way, right away, right now.... And screw anyone else.
I had one family just drop off their son and leave when *I'd* arranged childcare for my older son (read theirs was a toddler), when I was high as a kite on painkillers following surgery, and another when I had food poisoning.
Their attitude was the same... It "should" be okay, because they say so.
I call it Queen of Hearts Syndrome ( or QoH Delusion).
I've learned painfully that there is just no getting through to these people, as they don't live in reality, and other people, simply put, are just not 'real' to them.
It's a close cousin to 'Since you're not doing anything' people who assume being a SAHP means you "should" be able to watch their children for them (free or paid) when ever they durn well please. <rolls eyes> Right.
ROFL... Actually, in the beginning of that learning process several years ago I posted on that (SAHP does NOT = Babysitter), and got an overwhelming response.
This woman is and has been using you (from your prior posts). MOST single parents I know are on the ball as far as childcare (aka backups or arrangements with work), the same way that most working parents don't assume that SAHPs are not 'doing nothing'.
But there are a LOT of Queen of Hearts out there.
No wonder her son has issues. Treating childcare providers as of she's doing them a favor, and demanding they change their business model to suit her wants ... Probably means he's had a LOT of them over the years, in addition to learning by watching how to be disrespectful and dismissive.
My .02.... You informed her you would not be able to watch hr son until x time today well in advance. OF COURSE she's going to show up and try to drop him off. Giving notice PLUS not letting her manipulate you ($20 says she'd just drop and drive leaving you the option of watching him or taking him to the police station) by not physically being there is a good plan.