Sorry to be blunt and maybe seem a bit insensitive but from my perspective it looks as though your girlfriend has a problem with honesty. I'll be devil's advocate and question whether she is just using the word "poly" to fuck who ever, whenever she wants.
There is always the option of repeatedly trying to make it work, but if deceptive behaviour repeats itself then eventually you've got to consider that maybe you are being used. If that is the case, look after yourself, there's better out there.
Playing the Game of Life with Monopoly rules.
Monogamy might just be in my genes
Poly Events All Over