After purchasing the Groovy Grove dungeon perk and coming to this tutorial step, you'll have to abandon the active Groovy Grove dungeon (if any), then re-enter the dungeon and on the left sidebar will be your different dungeon levels to choose from which should include Groovy Grove II.
After purchasing the Groovy Grove dungeon perk and coming to this tutorial step, you'll have to abandon the active Groovy Grove dungeon (if any), then re-enter the dungeon and on the left sidebar will be your different dungeon levels to choose from which should include Groovy Grove II.