Maybe someone else has said this. I haven't read the whole thread. Turn the tables here. If you were going to take a week's holiday to somewhere like Las Vegas with some of your guy buddies would she take that as a code term for cheating? If she did and told you you can't go how would you react? Looking to the future, is it going to be the "rule" in your relationship that a) she doesn't go away on overnights unless you're there too, b) you can go away on overnights even if she's not along, c) neither of you goes away overnight without the other with maybe exceptions for things like family visits?
And while you're pondering this, you might want to look a bit further into the future of what's going on between you two and what implications not "letting" her go has. Maybe she's impressed with how much you want to be with her. Such women exist. Maybe she begins re-evaluating your relationship with you because she begins seeing that being with you means not being able to do things, mostly social things, she's normally done because you have a problem with it. Maybe she begins to see you as too insecure and less attractive. (I've read here and there that self confidence is a powerful aphrodisiac and you're not showing a ton of it here.) Maybe she's insulted that you don't trust her. Maybe she tells you to piss off, says you have no say in this at all in this.
And if you're giving her the message that a briefly extended time away from each other means cheating is likely or at least possible why would she not think that you won't be above playing around while she's gone? For my part, if I was seriously involved with a woman that I didn't trust to be away with friends for a few days without me I think I'd have to reconsider whether I should stay in the relationship.