I'm going to put this nicely, because I've been in the same position.
I can totally believe that he has pursued you for the money, and tried to be intimidating etc
And this has made you paranoid.
I really can't see him deciding to send his children, so presumably at an expense of at least £20k a year in order to intimidate you to pay a bill. If he'd been seen looking round, or hanging round outside the school, okay, but not actually going to the trouble and expense to send them to the school - and knowing that you were there first so will have got the story in first.
If he's intimidating you for doing a bad job, then it's pretty high chances that he has, and will have others to intimidate as well. Will he move his children round to different schools?
It's really easy in this situation to see everything they do as a deliberate attempt to intimidate. I've been there, and I would run things past someone who was fairly neutral, and knew the other person well, and they'd say if they thought it was a fluke or deliberate. Those that they thought were a fluke, which tbf weren't many, I had to deliberately set to one side.
So what I'd do is ask to speak to the safeguarding lead, and possibly the head, and give them your side, without exaggerations. So if anything happens then they have the heads up.
Then stop. Don't go round telling people, don't shoot daggers. Just get on with ordinary life. Maybe ask a friend if they can stay with you during pick up just in case.