Well, things didn't go quite as well as they might have but in general the right things happened.
PRIORITY #1- you gave the sitter and the kids enough time to make it into the house and safety.
I used to live in Georgia where we have these gigantic marsupial rats known as 'opossums'. I believe the name comes from the typical southern phrase people utter when they run over some sort of animal in the road. Thunkthunk!" Oh!... possum!" WHen threatened sometimes they will hold still, which can be a viable defense since those hideous snaggle-toothed vermin have outlived dinosaurs, British rule, and bellbottoms. In your case the same sort of strategy worked but I would suggest a more active role. Playing possum works sometimes but there was this kid, Lloyd, who lived next door, and if he found a possum, moving or not, he would get some lighter fluid and...
well, sometimes standing still doesn't work.
I like the pepper spray idea, personally. We had these other critters which other folks on TFL have encountered, called skunks. They use something similar and although they haven't been around as long as possums, they seem to be doing pretty well and I sure as He!! wouldn't mess with one. My neighbor Lloyd tried it once, though, but it was only that one time. Lloyd may have flunked the third grade twice and never could remember his multiplication tables but he remembered about the skunk after that.
- I am not mocking you, just trying to lighten the mood. Seriously, I am glad everyone is okay. Do something nice for the sitter!
Things worked out pretty well with the kids (ages?). You might want to go over a plan with them and the sitter in case there ever is another similar occurrence. Make a plan so the kids know what to do. You might have them duck down out of sight if a hostile person approaches the vehicle and you are not near the house... You may include it when you train the kids what to do in case there is a fire in the house, someone gets hurt, etc... It's sad when you have to train your kids to deal with such a situation but forewarned is forearmed.
In this case I would try to talk the guy down, be reasonable but firm and keep some distance between you. If he approaches then warn him to keep his distance LOUDLY. Make plenty of noise so that if there is anyone around then they will hear you and come to help. Sounds like this guy made plenty of noise on his own, though. If he continues then since you can't leave the kids, present spray or pistol and warn again. If he attacks then defend yourself and your kids however you can.
My two cents.
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Those who use arms well cultivate the Way and keep the rules.Thus they can govern in such a way as to prevail over the corrupt- Sun Tzu, The Art of War