Arrange the gummy worms in a 12-compartment ice tray, letting them hang out over the edges of the tray. Fill with root beer and freeze at least 4 hours or overnight.
With a small ice cream scoop, fill the bottom of a one gallon punch bowl with scoops of both frozen yogurts, using the full container of each. Very slowly fill the punch bowl with root beer; it will foam up.
Float the wormy ice cubes in the top of the punch. Fill each punch cup with a scoop of ice cream and an ice cube. Float additional worms on top of the punch or in each glass.