AITA for a girl getting hurt at my little sister's birthday

Before I get too far into this, I'd like to say I'm looking for answers to the question "Am I The Asshole" not "Am I an irresponsible idiot incapable of thinking things through" because the answer to that question, is 100% yes. I am.

I (F17) was left in charge of my little sister, who we'll call Avie's 14th birthday, while our single dad is on a cruise. This has been the plan for months, and I had multiple conversations over the months with Avie about what she wanted. At first, she wanted to go to a Noah Kahan concert.. I lost the ticketmaster war. We ended up with her and 5 friends hanging out at her place, having burgers, and a great time, hell yea!

The day arrived, one of the 5 was already there from spending the night before, and Avie was super excited. With a single dad of 2, she's had some not great birthdays over the years, and since moving into a HOUSE, she was so hyped to have friends over to her place to celebrate her. They all got to our place around 1PM, which was a mistake on my part, because by 5PM, 4 hours of celebrating, giving her gifts, eating and talking, they were all quite bored. Whoops. Avie and them talked and came up with an idea to go to a trampoline park. Seemed harmless and fun. Called them up, was able to get reservated to have an hour. Shot my dad a text to let him know about it. Left on delivered.

We all were having a great time when one of the girls, who we'll call Bella, went down, holding her ankle. We got her help, turned out to be a grade 2 sprain.

Now, before talking about the end here, I want to say that Avie was still super happy, she had fun with friends, got to have them all over, saw a friend that she hadn't seen all summer, and I surprised her after everyone left with Noah Kahan tickets. Me, her and Dad in San Diego.

The problem is that Bella's parents were quite pissed. They didn't know me and didn't care to hear my endless apologies and owning up. Apparently, their gymnast daughter hurting her ankle on a freak accident, is worthy of her dad cussing me out in front of Avie. I apologized to Bella one last time, told her parents to act like the adults, and left. My dad was quite pissed that I took her to a "dangerous/active" place without his permission and was worried about her parents suing before I told him they couldn't (and aren't), he isn't as mad now, but still was providing 0 comfort. Avie came up to me the next day and told me she loved me and that I tried my hardest, and it made it all worth it though.

Am I an asshole? Should I have stayed and listen to their berating? Am I playing the victim instead of taking accountability? Idk I'd like to be told thanks