How do I go about not inviting someone on vacation?

I'm going on vacation with a friend this summer. We have a mutual friend with whom we are pretty close, but she's, well, kind of a downer when it comes to trips. She's the kind of girl that will have a fight on the phone in the bathroom for an hour with her bf while we're waiting to go see the Space Needle. If we tell her to come on, or maybe, "We'll just catch up later," and go without her, she'd be so mad.

She is one of our closest friends and as much as we love hanging out with her, she's just not a good travel buddy (as seen through trips she's taken with others and her sudden moodiness on occasion).

We've considered inviting her, but I'm the one who thought up the trip and invited my first friend, so it's my decision. My first friend doesn't have a problem inviting my second friend, but sirens are going off in my head not to bring her along.

Should I invite her anyway? If not, how do I explain myself to the second friend? :\