"Doesnt it seem that there are other constitutional interests that could be argued in this sort of case?"
Yes, I think so. The problem, as I see it, is to even get a court to agree to interfere in internal religious matters so these arguments can be heard. The arguments don't mean much if the case is thrown out before it gets to trial.
The situation may be different for the divorce case. The court might not care if the wife has been influenced by third parties, but it might be very concerned if the wife will subject the children to an environment that slanders the father and treats him like the worst kind of person.