How can i convince parents?

I just went away on a state theatre competition trip for a few days. When I got home, I got grounded because I didn't call home enough (I've called home twice and texted a few times whenever i couldn't call). The problem was that we never had free time and were always super busy going from one thing to the next, and by the time i got back to the hotel room, i always crashed and went right to sleep, then did the same thing over again the next day. I tried explaining to my parents that it was very tough making a call home because we were always busy or that it was too loud to hear anything over the phone. They said that it's just an excuse, but they won't believe me when i said that most of my friends only called home once or twice. They also said it was disrespectful not to call home even when i did, but it was only twice. so they grounded me and I've never gotten grounded before, and I'm a responsible 16 year old and I don't understand why I'm being grounded. I've gotten my phone taken away and I'm not allowed to go to a party and I'm not allowed to go out with my friends for a big group date with my crush. How can i convince my parents to let me off for the group date? I've already tried talking to my mom about it. I've kept calm but I started crying because I feel like I can never talk about anything with her. She always pounces on me and jumps to conclusions before i can finish a sentance. so i'm thinking about asking my dad about it again because he actually listens to me before saying anything. how can i ask him to let me off for friday?