What is the ruling on children staying out until ten o'clock at night for Maghrib prayer and midnight for Isha prayer, given that they must go to school early?

Allah has made prayer obligatory upon adults, but it is not obligatory upon children. However, their guardians must command them to pray when they reach the age of seven and strike them for it at the age of ten, as the Prophet (peace and blessings be upon him) said: "Command your children to pray when they are seven years old, and strike them for it when they are ten years old, and separate them in their beds."

The wisdom behind this is to accustom them to prayer.

Therefore, the two children must be commanded to pray on time so that they become accustomed to it, especially since they are approaching the age of puberty.