What are the father's obligations after divorce regarding the fate of the children (seven years old and two years old), especially with the mother's desire to reside with them in her country, and the father's fear of the impact of that on their Islamic upbringing?

You are responsible for raising and educating your children, and you have a greater right to their custody in the event of divorce if their mother does not reside in your country, and you believe that their remaining with you is better for them. Therefore, do not relinquish their custody.