Aspire - direct one's hopes or ambitions towards achieving something. impend - (of an event regarded as threatening or significant) be about to happen. inspire - fill (someone) with the urge or ability to do or feel something, especially to do something creative. try - make an attempt or effort to do something.
In this context, I believe aspire would make the most sense.
Explanation: throughout the story it shows that the all race inclusive restaurant is challenged by the social ideas of the are proving that the family will uphold their beliefs despite all the challenges that come with it