Quick questions: javelins with dueling style and natural weapon proficiency

[JNAProductions]

You are not attending to the fact that the Dueling fighting style also requires that the weapon be "in one hand" when damage rolls are made. Ignoring that fact is a clear and unequivocal violation of that rule. What rule in the PHB gives you permission to ignore the Dueling fighting style rule?

Wielded in one hand. Not held, wielded.

Where does the game give you permission to change the status of a wielded weapon mid-attack?