How much of this is meant to depict Lucy herself being stubborn, and how much just a very young kid rebelling against her parents? I think often, in Peanuts, cases of the latter evolve over time into cases of the former. That is, strips intended as general observations end up getting sorted by character, and so the kids accrete characteristics over time and in this way become complex.
In the lead-in panels, Schulz shows Lucy being contented with a word balloon containing a musical note. I suppose it's meant to represent her humming. It's not the first time he's done this.
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