lol well, it would make more sense to break up with her beforehand rather than after. This way any connection you had with your girlfriends brothers girlfriend (spaceballs!) has been severed, on paper at least. On paper she would just be some random chick your hooking up with in some other random chicks house and not really an act of betrayal.
This is how I would rationalize it. Otherwise its just bad. Its probably bad either way but I'm looking for some kind of loophole.