Offline/Appeal to her disinterest and invite her to join you
"So this is all pretty lame, huh?"
She shrugs. "I dunno. I mean it's not where I wanted to spend summer vacation."
"Trust me, it's pretty lame. I've been here before."
"Really? Out here?"
You nod as coolly as possible. "I helped find this place. And you're right, you shouldn't want to spend your vacation here. This whole place hasn't been used in forever. People stopped coming for a reason you know."
"Oh yeah? Why's that?"
You snagged her interest, but you can't follow that up with anything. You have no idea why the place was abandoned.
"Umm... Doesn't matter. So anyway, I thought I'd help you out. There's only one cabin that's any good. It's small but it's out of the way. If you take that one you can at least avoid everyone else for the week and pretend like this week didn't happen."
"Oh. Okay. I guess mom and I can take it."
Crap.
"No, um, it's my cabin. But I was going to let you share it with me."
"You want me to bunk with you?" she asks skeptically.
"Yeah. Only because I thought you might appreciate being able to hide for a week. You could read as much as you want without anyone bothering you and there's only so many cabins to choose from. I'd rather pick you for a roommate than get stuck with anyone else."
She takes a moment to consider your argument. You can't remember if she has any siblings, step or otherwise. Bunking with a boy might be weird for her. But she doesn't take too long to come to a decision.
"Hey mom," Nicole says over her shoulder. "I'm going to bunk with Justice this trip, k? He knows the camp so he can show me around and make sure I'm okay."
"Well isn't that nice! Thank you Justice, that's very sweet of you to offer!"
"Yeah!" you nod with a grin. "But call me Jay," you say to your aunt then lock eyes with your cousin.
You continue the conversation a little, but Nicole may have agreed to stay with you on the premise that you wouldn't be spending time together, preferring to read in the cabin the whole time. Kinda sucks if you don't get any time in the cabin to yourself but you can't do much about it now. She's at least nice to you though and pretty easy going so you should be able to get along well enough.
After a few minutes you awkwardly separate and go back to your respective seats. You inform your parents about Nicole bunking with you and they both approve of your choice of roommate. A sense of satisfaction washes over you as you realize that this week might still turn out okay after all.