Is what the husband did—withholding maintenance from his Christian wife who takes their children to church and prevents his relatives from influencing them Islamically—correct, or might he be held accountable for it before God?

First: Marriage to a Kitabiyah (Woman of the Book) is permissible, but it is fraught with risks, especially regarding her influence on the children's beliefs and religion, particularly if she resides in non-Muslim countries.

Second: You must safeguard the religion and morals of your children. You should strive to gain custody of your children by all means, as the laws of those countries might grant you this right, and a disbelieving woman does not have custody over a Muslim.

Third: If you are unable to achieve this, then strive to be close to them as much as you can, and prevent her from taking them to church. Surround them with a Muslim environment. If you cannot do that, then there is no blame upon you for restricting her financial support until she either leaves your children with you or refrains from accustoming them to the church.