From a girl perspective, this is asshole behavior. You (albeit begrudgingly) agreed to commit to girl #1 and she said she would rather let you go than be open, and then you went against that by keeping something going with another girl. Yes, you do need to end it, but I really, really doubt you are going to end up on good terms if she flies up and sleeps with you a few more times before you do end it. There is no good way to deal with this situation. She will feel cheated on because you in fact cheated on her. You should be honest and upfront and break it off in person and then she is stuck with you for the weekend so you should really start thinking of how to smooth that over.
If I thought I was in a closed relationship and they broke it off and it turned out they'd cheated just before and decided to do the right thing only after a few last f-closes, I would be livid.