Is it permissible for a Christian wife to stipulate that she takes the children to church and has them baptized in exchange for her agreement that their father takes them to the mosque, knowing that they reside in the wife's country?

This condition is not permissible, neither in the marriage contract nor after it, because it contradicts the Qur'an and Sunnah. It is not permissible to agree to it because it involves the children going to church and associating partners with Allah. This condition is void, as the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions in what is made lawful." Therefore, it is not permissible to fulfill it. If the wife is not satisfied except with this condition, then there is no good in her, for Islam is supreme and nothing is supreme over it anywhere, as the Prophet, peace and blessings be upon him, said: "Islam is exalted and nothing is exalted above it."