In a manner characteristic of dandling; in a gentle, playful, bouncy way.
From dandling (the present participle of dandle) + -ly (the adverb-forming suffix). This creates an adverb that describes how an action is done with the quality of dandling—gently and playfully.
Dandlingly is theoretical—you won't find it in actual use—but it's a perfect example of English's infinite expandability. Any verb can become an adverb if you add -ing and then -ly, creating words that feel right even if nobody says them: 'she spoke dandlingly' is grammatically perfect but absurdly specific.
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