Is my act considered disbelief (kufr) when I hit my sister's headscarf, which had "There is no god but Allah" written on it (and it was upside down), to prevent her from entering the restroom with it, and not out of dislike for the word itself?

You must turn away from doubts (waswasah) concerning disbelief (kufr). What you mentioned does not constitute disbelief. However, seek forgiveness from your sister for hitting her. There is no harm in wearing something on which the name of Allah is written, provided it is protected from disrespect. So, it should not be placed in an unclean place, nor should one enter the lavatory while wearing it, out of reverence for Allah and His rituals. It has been narrated that the Prophet (peace and blessings be upon him) used to remove his ring when entering the lavatory, and the engraving on his ring was: "Muhammad is the Messenger of Allah."