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Re:Dungeon Scrawl: Old school maps in minutes by sronors on Tuesday June 23, 2020 @11:54PM (#23623901)
Not sure if it fits your requirements but there are games like No Thank You, Evil from Monte Cook Games. It is geared specifically toward kids.
Re:Dungeon Scrawl: Old school maps in minutes by prawn on Wednesday June 24, 2020 @12:10AM (#23623999)
That looks vaguely like it could work, if there was a system to borrow from it. My kids responded really well to a very literal "exploring a cave" scenario so don't necessarily need the less-D&D style of those stories.

We also have a house full of toys so I'm trying to avoid buying more gear. We already have paper, pencils and dice.