This is too funny.
Cougars must be meaner/more scary in Texas. Here in Oregon we have lots of them, including several in my area, and I've never given it a second thought.
They will occasionally snag a pet, and I startled one once while it was stalking a deer in a thick fog, all I really saw was a blur and a long tail
I'm a mile from the local k-thru-12 and they captured two wayward cougar kittens/cubs at a park half a mile from it. No outcry to kill the big cats and save the children yet
What the OP has described is fairly NORMAL cougar behavior, if it was abnormal or threatening behavior it would be a different story. Your normal/average mountain lion, statistically and in practice, is pretty harmless to humans, even children. Of course you will do as you please, but in my mind you are overreacting somewhat.