It is the past tense of the word <em>vie</em>, with means to compete with great enthusiasm and eagerness for the reward or achievement. Here it is used to express that the <u>daughter is competing for the spot on the squad with high spirit. </u>
<u>Because of that, it can be changed with the word </u><em><u>tried </u></em>– <u>she is trying for the spot on the team, trying to compete against other candidates</u>. While it takes out the idea of great enthusiasm, changing <em>vied </em>to <em>tried </em>still carries to message that the daughter is attempting to get into the team.
