Is the second sentence a transitive one? No.
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tinanam0102 Kids dillydally their way to piano practiceAlthough it is unusual, this may be the intended sentence. I don't think that it has to be a case of a missing word. This could be an unusual X's way construction.
tinanam0102Would you tell me if 'her way' an object in this X's way construction?I would, and I will, and it is. Yes, it's an object.