In order to answer this I think we need more information. First, why does the girl live with her non-custodial parent? Is it because she doesn't want to live with her custodial parent? And if that is the case, why?
a. If it's a valid reason, then Parent 2 should accept that if s/he cannot or will not accept the parental obligation of being the custodial parent then s/he doesn't really have the right to interfere in what Parent 1 decides.
b. It sounds like perhaps the girl WANTS to stay with her boyfriend at his house while Parent 1 is out of town and if so then that's probably why Parent 2 was never asked. I think a 17-year-old girl staying in the same home with her 19-year-old-boyfriend is a recipe for disaster. You know what those two are going to be doing in the dead of night.
c. Parent 2 should definitely have been considered as backup parent in Parent 1's absence. Of course, that assumes that Parent 2 is not unfit in any way and that the girl and s/he get along. If there are hard feelings between them however, it's understandable that Parent 1 would be hesitant to send the daughter over there...especially if she's pushing to stay with her boyfriend.
Bottom line, this isn't a six-year-old we're talking about but an almost-adult. If she's untrustworthy enough that she can't be left alone at that age, then she probably doesn't need to be at her boyfriend's house either. Unless staying with Parent 2 would be unsafe or miserable for one or both of them, I think that Parent 2 should insist (and as custodial parent, could) that their daughter stay with her/him.
-frolix
(And this is a perfect reason why pets are better than children.)