Does not wearing the complete legal hijab—due to parental prohibition and the purchase of unsuitable clothes—constitute polytheism or following one's whims, especially since the questioner is dissatisfied with this situation and strives to complete her hijab?

Following whims is not polytheism with Allah Almighty, for polytheism is associating partners with Allah by directing acts of worship to them, and the religious texts have clarified this. The hijab is an obligation that a Muslim woman must adhere to, and if the parents reject it, then there is no obedience to them in disobedience to Allah, while it is still obligatory to honor and be dutiful to one's parents.