Just need to vent about a co worker. I am very angry.

So, i work at a daycare and i am the cook and most days, help in the classroom in the afternoon when i finish the lunch duties. Yesterday, a coworker and i were scheduled to be off at the same time. We realized 15 minutes before that time That we could move 1 child to a different room then one of us could leave. We were outside at the time so my coworker took the one child and moved her back inside. I was expecting her to come right back out and ask me if i wanted to leave first or if she could. Well, she didnt...she just left. When 2 of us are scheduled for the same time and one can go early, i feel like it needs to be discussed between the 2 people which one leaves first. So that was really annoying. Then today, me and this same co worker were scheduled to leave at the same time again. Which was 2. For me, since i am the cook, that usually means i can just leave once i finish the kitchen stuff. Which is what i was planning on doing. So i was starting to clock out at 12 50 and i was going to go grab lunch, run an errand, then i was going to come back and pick up my child, who was napping at the time. My coworker saw me clocking out and asked me if i was leaving....i said i was going to get lunch. She said o. I said why, am i supposed to be letting you go first? She said, yes because she got there earlier than I did this morning. I am too nice of a person. Because i had to clock out for a 30 minute lunch break, just to come back and clock back in for 40 more minutes to send her home. So that was really annoying. But then i got to thinking later on, that we were both scheduled for the same time and she left before me yesterday, so today it should have been my turn to leave before her. The situation of it is super annoying. But actually staying wasnt a big deal. Its the principlesof the situation that makes me angry. Im also really mad at myself because i didnt stick up for myself. If this happens again with this coworker, i am definitely going to speak up that it is my turn to leave early. I feel like im going to get some clap back with people saying that i also should have discussed with her today who was leaving first. Which i can understand. But my main job is the cook and when im scheduled for 1 30 or 2, it ALWAYS means i just leave when i finish chores. Everyone at the center knows this is how it works. I feel like it was wrong of her to expect me to stay for her, when we were both sheduled for the same time. My work was done. I dont know how or why she was in charge of deciding who left first. Ughh...