The word "obstinance" (often spelled "obstinacy") refers to stubbornness or the quality of being unyielding or difficult to manage. The correct usage of "obstinance" is in the sentence:
"Sheila's obstinance meant she refused to do her chores even after Dad told her she'd be grounded if she didn't."
This sentence correctly conveys the meaning of the word in the context of stubbornness.