A family member wanted to take a pic of the god mother and I with our God child, we thought it a normal request.
I don't see anything particularly abnormal about it. I think that's a valid request.
The ex using that as a reason to dysregulate seems to me quite typical in the sense that they can take anything an use it to dysregulate themselves. On this basis, I think yes, we do add to their own highly negative feelings when we are involved in some way.
After noting your ex used that to dysregulate, it might be helpful to you to note then that you "decided" to manage that to the extent that it was enough to be "unforgettable" to you.
Specifically here, I think you added to part of the cause of her feelings by being one of three people in a picture that she felt "terrible" about. Also consider that the BP, the godmother, and the godchild all had some role to play in making said BP feel "terrible" as well. So why do you have to manage the BP's "terrible" feelings?