I have no doubt that the parents staying calm plays a huge part in these situations, but I KNOW WITHOUT A DOUBT that prayer worked. It's just that simple for me.
Because, it couldn't be that, at that particular time, your presence was more of a comfort than your wife's presence? Or, even that seeing both parents calm was more reassuring than seeing one parent calm? Or they just tired themselves out? No, must be God, taking time off from not feeding hungry kids in Africa to make sure yours took a nap.