Thank you all for your comments and replies. You have confirmed my belief that this woman probably should not have a place in the leadership of our Troop. The ASM and his family are some of our closest friends and I wanted a few other opinions before I made a decision. I wanted to make sure my personal feelings weren't clouding my judgement. And, like I said, there is quite a bit more to the story.
I'd like to be clear that I am not questioning that she is hearing from God. That is something the ASM will have to discern for himself and since he is a man of deep Christian faith, I do not worry about him or his kids. His oldest son just earned the God and Life award, and the youngest was recently baptized (in the Jordan River no less) after earning the God and Church award. They will discuss as a family and likely learn great lessons from this. His concern was not even for his own kids, but for other kids who might not have the same faith, support, and personal strength.
We are not chartered to a faith group. We are chartered to a non-sectarian private school. Our scouts include Christians, Catholics, Mormons, Hindus and Muslims. Something said to the wrong family and in the wrong context could actually result in the school revoking our charter. I would absolutely risk losing one scout if it means keeping the program alive for the other 29 boys.