Every time my three-year-old bashes the keyboard randomly my hot corners stop working. What key combo is she pressing?

You can search through the keyboard shortcuts with System Preferences -> Keyboard -> Shortcuts.

For me, "Turn Dock Hiding On/Off" is Option ⌥ Command ⌘ D

I don't see a keyboard shortcut for enabling/disabling Hot Corners (in High Sierra), though maybe your list is different?