I would have to respectfully XXXXX XXXXX your girlfriends therapist on the point that you have obviously succeeded in making a blended family work. That is healthy and as you said done not to maintain the primary relationship with your ex but for the purpose of being part of the influence on your children. That is different.
The fact that your current partner has issues with all of this are not going to resolve. I have seen this scenario many times, and to her credit, she has needs and desires that are not necessarily selfish,however, her needs are not going to be met in this family situation that you describe. You have to be very honest with her in your desire to maintain the path you have followed with the blended family and she will have to make a decision as to whether she can tolerate this.....which because she feels like an outsider, I doubt she will be able to tolerate. In family systems we refer to this as a triangle. You, her & the other (meaning you ex - and blended family. When a triangle exists, someone is going to feel left out and want change. In this case, I see that she is the only one that will make a lasting change and that will be to move on from the relationship. The power of the family it to great for her to absorb.
If you have additional questions of me, feel free to ask.