Should i quit my job while i am in high school?

okay so I have this job and I am still in high school. Around my age everyone started getting jobs and I was so tired of asking my mom for money because it made me look selfish, so I got a job as a waitress. I loved the job over the summer, made a lot of money, even paid for a new phone within a few weeks. However, there is this one day where I desperately need off for a family occasion my parents don't want me to miss. So I asked everyone I work with they all told me no and then one guy just didn't want to do it because he would be working 5 days in a row (I was really pissed off about that) so two girls I worked with told me to come in the next day and talk with my manager who deals with scheduling. I went in and she pretty much told me that she wouldn't help me and that I have to keep looking even though I asked everyone I knew there. She told me she would ask another person to work but it wasn't a given they would do it. I can't call out that day or else they get mad and might fire me. I am starting to think this is a little ridiculous and I already see now that in december and march and june I'm going to need a lot of days off and I might not find coverage. My mom is suggesting that I just quit the job and focus on my schoolwork and extra curricular activities which include dance and band (music is my specialty) so should I stay with the job or just quit I'm in a fix here and I really don't know what to do. PLEASE HELP ASAP.