Careful reading makes it clear that the children were given the mouse to eat, not actually directed to eat it. Presumably the intention was to provoke the response - 'No, I honestly won't wet the bed, ever again, Only don't make me eat the rotten mouse.'
However, given the nature of Elizabethan medicine we cannot be sure. People were regularly pouring down their throats water distilled from other people's body parts, oils derived from boiled frogs and toads, powdered snail-shells and fish-bones and glass, and goodness knows what else. It is not unlikely that some brave children took a deep breath and a courageous bite of rotten mouse, and no doubt were very, very ill. And were treated appropriately.