Black Hole Girls- I only mentioned this game for one reason. Namely, in BHG, you play as a 12-year-old girl with a pet alien supermonster. The thing is, you roll different sized dice based off of who has more control in the relationship, the girl or the monster.
There is a dice distribution that looks like this:
When you start, you pick for one side to use 1d6s and the other to use 1d8s. Through-out the game, you adjust the dice sizes along the scale; if you increase one side by one step, then the other drops by a step, and vice versa.
Where am I going with this? You can have a similar mechanical back-and-forth between the teddy bears and the monsters; it would make for a good "oh crap" moment for the players, at least, when the dice they are using drop from d8s to d6s, or worse, when the child they are guarding starts having a nightmare. Or, maybe tie it to the time of night, so that your strategy has to shift through-out the night...