Can I use Bad Toys on other people's babies?
I finally took the time to ask directly on the Wyrd Games forums and someone from Wyrd responded:


  Yes, you may discard a bad toy to make any baby in play (including your opponent's babies) take unsupervised actions.


So the answer is yes, bad toys can be used to activate an opponent's Evil Baby's Unsupervised Action on your own Activity Step.