Is a father's waking his two children, aged 10 and 13, for Fajr prayer at 3:30 AM, followed by their returning to sleep and having difficulty waking for school, a correct action or premature?

The Prophet (peace and blessings be upon him) commanded children to pray at the age of seven and to be disciplined for it at the age of ten. Therefore, parents must wake their children for Fajr prayer and the remaining prayers, and continue to do so, while ensuring they sleep early so they can wake up actively. They will get used to this over time.