Damn, I hate what this cult does to kids!!
You mentioned you had custody. Where I live, there are legally differing kinds of child custody -- full custody, sole custody, shared custody -- and they each have their distinctions and legalities.
Have you a lawyer? Can your find out what your legal rights are in this regard? Can your son be helped to be "neutral" until he is of legal age?
Also, do you know what the assembly part might be about or what is the point of his part? If it has anything to do with living in a "divided household", that could be very defaming to your character, to which you could strenuously object and threaten legal action....
I feel for you in this situation, not easy. No easy answers.