I feel like it's his responsibility to set boundaries with this woman and creates reassurances (WITHIN REASON) for you that you are still the primary and therefore, priority.
This stuff ain't for the faint of heart. You need to look at yourself critically and try to suss out whether or not you're handling this in a mature, reasonable manner or indulging jealousy. He needs to be dead-honest with himself about whether he's allowing his feelings of twitterpation to put priority on the other lady and neglect his responsibilities to you and to being a decent partner.
It is not unreasonable for you to feel put-out that he didn't uphold the terms of your agreement that he "give it a rest" on your birthday.
I think the key here is to not be ambiguous about the details. You must work out with him exactly what you need and exactly what is reasonable based on his relationship with the other woman.
I also think sunshine is a good thing here. He may be uncomfortable with he idea of you and she meeting, but I urge him to work through his inhibitions about it and try to push himself to make it happen. The point here is having a healthy relationship with both of you. Like I said: this isn't for the faint of heart and if meeting her is what's required for this to be healthy, I think he should consider it.
"Although the most acute judges of the witches and even the witches themselves, were convinced of the guilt of witchery, the guilt nevertheless was non-existent. It is thus with all guilt."
How can you claim to love someone with all your heart if you can't stand to let them love with all of theirs?