Are you sh*ttin' me? You don't know what to do? I'll tell you what your situation is.
A) A company trip and he can bring a guest: He stipulates MUST BE FEMALE. He's a lying bastard.
B) Any guy going on a trip will invite someone he wants to score with over any of his best friends. He wants her.
C) This guy is trying to mack your girl.
D) Challenge Guy is an idiot for even suggesting that letting her go is "Being a man".
You need Put your foot down hard. Let her know that if she goes, you won't be around when she gets back. It's something you DO NOT DO. She might have no intention of cheating on you, but that's not the point. The point is, the other guy DOES have intentions beyond friendship. Ask yourself, if you were in a similar situation, you have an extra ticket to Maui. You could ask any of your friends, let's say you're BEST Friends with a girl that's around a 6/10. But you're good friends with another girl that's a 9/10. Who are you going to invite along, and why? Exactly. I'd suggest having a talk with this f*cker and let him know that if he pushes it he's going to find himself chained to a bed in a cheap motel and a big black man in a crotchless batman suit is gonna rape him over and over while he squeals like a little girl in a blender.
If she goes with him, she's gonna f*ck him. Then give you the, "We were drunk, it just sort of happened, it didn't mean anything... any of the 18 times we did it, honest" speech.
You could always pull a total Deagler maneuver if you want to really screw this guy over... Tell her she can go, she'll tell the guy, the guy will blow his load. Then buy yourself a ticket and make it a threesome.... oh but there's only 2 beds in a hotel room... F*ck her hard while he's in the room!
Deagleclaw out.
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No matter what comes, walk like a man. - Al Lan Mandragoran (Wheel of Time)