Offline/Cover her
You decide to risk waking her and do the nice thing. Carefully stepping through the minefield of sleeping cousins, you make your way over to the very exposed girl and crouch over her. Gently grasping the hem of her nightie, you slide it down her slender frame. You almost manage to cover her modesty before it catches, bunched up under the small of her back. Holding your breath, you give a slight tug to release the bunch and look up to her face to check if you were successful. Her wide eyes state up at you as her sleepy mind tries to piece together what is happening. You hold a finger to your lips to keep her quiet when she looks like she might cry. You quickly tug her nightie down all the way, no longer needing to worry about waking her. Her face changes several times in a few seconds, no doubt sifting through several sensors to explain why she woke up with you holding her dress above her waist. Thankfully, her face settles on a blush and she turns away, trying to hide in her pillow.
You leave her there, throw on some clothes, and open the cabin door, but stop when something attaches itself to you. "Thanks." your cousin mumbles, muffled by she speaking into your leg.
"Don't mention it." You really hope she doesn't. She seems to have come to the right conclusion about what you were doing, but you fear how the story might sound in retelling. You venture out into the camp with her still clinging to you.
Most of the camp still seems to be asleep, only the birds and Uncle Dave are making any noise. Uncle Dave being up means there's coffee brewing, so you make your way over to him and he silently offers you a cup which you accept.
"Yulia, you're up early. Want some cocoa, darling?"
So that's her name! Yulia nods to accept the cocoa and snuggles into your arm.
"Glad to see you two are getting close so quickly. Here you are Jay." He hands you a tin mug of coffee with a sugar and powdered creamer just the way you liked it last time you were out here discovering the camp, then turns back to make Yulia's drink.
Yulia buries her face in your arm. "Well, he saved me." She had to mention it. Maybe he didn't hear since she was muffled.
"Saved you, huh?" The man's got sharp ears. "From what, a bear?"
Yulia tries to disappear into you.
"Oh, I get it. Still sleeping without underwear?"
"G-grandma says that girls shouldn't wear p-panties to bed 'cuz girl parts are s'posed to breath." She looks even redder explaining herself than when you caught her, though maybe that's just because the lighting is better now.
"Don't worry, I won't tell your mom. You can sleep naked for all I care, but I'm sure she would end up hearing about that if you did it here." He places the cocoa in front of her with a wink. "Thanks for looking after the youngins this week. I'm sure you got roped into it somehow instead of volunteering like the lady folk have said, but I appreciate it nonetheless."
While Uncle Dave continues to make small talk with you, reminiscing about your first trip here, the rest of the camp slowly wakes up. Your dad is the first up and joins the conversation with his own memories of finding the camp. Then your mom and a couple other aunts come out to ask about breakfast, so Uncle Dave begins orchestrating the morning. Naturally you get enlisted to help and Yulia does her best to follow along too. When it's all ready, you and your shadow are sent to wake the rest of the kids and bring them to breakfast.
Asha and Brayden's sister come back with you in their pajamas, but the rest stay to get dressed since they abandoned their pajamas. The three girls all sit around you to eat and you eventually figure out Brayden's sister's name is Beth. Your sister joins you before long, followed by May, then Brayden, and finally Nicole. It seems everyone wants to sit as close to you as they can, which means Nicole finds herself at the farthest end of the table since she was last. With your only viable conversation partner so far away, you are forced to listen to the little girls chatter around, thinking up all kinds of things to do that day. At least they are all talkative enough you don't have to really participate. You offer a few words here and there to imply you're listening, but you wouldn't be able to get much more in if you actually try. Eventually, you're able to tune them out completely by grunting on autopilot so they don't even know you aren't paying attention.
Breakfast passes quickly in this manner and you finish eating long before the talkative girls around you. Getting up to clear your dishes, you see your only clean escape would be to get involved with the cleanup efforts. However, you can't even wash your own plate before Aunt Clara shoos you away to go look after the little ones. It seems your role as babysitter is official now. Surely they would be fine without you, so it seems your role is less about keeping them safe so much as keeping them out of the parents' hair.
This is likely the last chance you'll have to fight this. Going along with it could afford you some more independence if they delegate all the supervision to you and let you out of other chores in exchange, but all that freedom will be wasted if you have to spend the whole week surrounded by kids. On the other hand, offering to do chores is bound to lead to more chores, not to mention a week surrounded by adults. In either case, you are pretty sure you can drag Nicole along so you at least have someone your age to talk to.