Isn’t Dreamwine the same thing that they gave to Robyn Arryn and Bran while they struggle through bad dreams?
I’m pretty sure they mix milk of the poppy into the dreamwine for Tyrion to lessen the pain. If it is the same drink that the maesters serve to little Robby Arryn, then it is not milk of the poppy directly, it’s something different that the sickly, or the medicated can’t use too often, or in large doses. In small doses, it induces sleep, in large doses, or freuqent doses, it kills people.