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.
 "Forge & Fortune"){kind=icon}
 "The Peacekeeper"){kind=icon}
 "Brave Shorties 2"){kind=icon}
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.