Take a break?

You're not a guy who should be the backup. If she wants to date others, then that's her choice, but only as long as she's aware that you can do the same. And, if she's talking a week long break, forget it. Breaks should be intended for those who need to find themselves, or make sure they have their priorities correct, it's not just to date other people. That break is just an excuse for her to cheat without feeling guilty about it, and I would hope that you're smart enough to not take that BS from anyone. She wants a "break" you'll give her a break up. That doesn't mean you can't get back together eventually (I would highly recommend that you don't get back with her however). She's looking elsewhere, and she knows it. And she's making it clear.

I wouldn't want to be with a girl who was always longing for someone else, and lookiing for any loophole to be with them.

Frankly, she's being a bit selfish. She's thinking she can take this break, fool around, then you'll be waiting for her with open arms, and she'll have you for the boyfriend support until she "needs to scratch that itch" again. She doesn't want you, (if she really did, she wouldn't be thinking about how she could be with other "cute guys") but isn't willing to lose you because you're the fallback. The backup. PLEASE PLEASE PLEASE don't make yourself the backup.

Tell her that you don't want her to go, but if she chooses to, it's her decision. But if she DOES go, you're either breaking up or you're not. If you AREN'T breaking up, then she's not to cheat. If she does cheat, and you find out, you're out of that relationship so fast it'll make her head spin. And if you are broken up, then she can do whatever she wants, but she can't expect you to wait with open arms when she returns. Balls in her court. If she wants the breakup, it was mutual, and you're better off without her. If she doesn't want the breakup, (I believe she does, as she suggested the pathetic excuse attempt at the word "break" being seperate from "break up."), then you both will continue dating, you will choose to trust her away from you, but if she's making out with other guys, that's officially cheating, and again, you're done in the relationship when she does that, and you're gone.

She's got to be prepared for whatever consequences she has from her decision (don't tell her that, as it sounds like a violent threat.), but there are other ways of letting her know that you will not take a lot of garbage from anyone, and she's got to make up whatever bed she chose to sleep in.

Now, since she's asking for the break, I'm thinking she's looking for an excuse to cheat. She's gone a week. If she were happy in the relationship, and if those eyes of hers weren't wandering, she'd have no issues with going on vacation for a week without any intention of cheating. She wouldn't have suggested it.

Understand that whatever she chooses to do, you have to take the high road. Don't seek revenge, but live better.

Good luck.

You do the same she suggested it take a break and do something new with other girls.She's either gonna leave to camp without telling you she did that stuff or she's going to camp telling you,Most couples that I know never pick up where they left of because they realize that there are better people out there but they stick to being friends good luck.

find someone better if she can't be there for you even hundreds of miles away then tell her not to have a break because the same situation happened and it just got worse dancers in high school tend to have a lot of on and off guys and believe there right about so just date someone else believe you'll find better cause I have

No matter how much you may wish you could please her, you're just not an on/off kind of guy. She's asking, so apparently she feels like it's your call to some extent. As much as some people hate to have a clingy person for a friend, I think there is more to lose by agreeing.
My logic is this. If you told her OK, you'd be lying and you wouldn't be able to look at her the same. If she wants you to say no, it's not right and you couldn't stand it, then you lose her if you say OK. Besides it's not a choice between you and camp. It's just that camp will be different than before. If she can't accept that, then what's in the future for you two?
So I think the truth is the way to go. If it's hard to say in words, then write it. Tell her what you said here. "I can't just let you go to camp and do all that, and then just pick up where we left off with the knowledge that you [did things]" Tell her it feels like cheating. You're not an on/off kind of guy and it bothers you that she's asking.
There's another possible approach, but I'm not sure it's a good idea. You can ask her how she would feel if you do the same while she's gone? It's only fair. Yes? You might save that card in case you say no and she decides to anyway.