This is between you and your boyfriend — not you and the other woman. The fact that he is taking photos with this other woman on his lap, and introducing her to his parents means that you’ve got competition! And that he knows it upsets you and still does it, means that he’s interested in her — it’s not a one way street. That means you have to compete with her for his attention, if you want to win him over. Consider what it is he’s getting from her, and what he feels like when he’s with her that he doesn’t get from you and his relationship with you — and focus on improving those “cracks” in your relationship. Guys go where they feel good about themselves, and if he’s getting something from being with her that he isn’t from being with you, he’ll go there. So use this problem to work on the relationship you have with him, and avoid the instinct to tell him what to do and ways in which he can and can’t behave, and instead… make him want to be the one who devotes himself to you.
I hope that helps. 🙂