What an interesting idea for a simplistic theme for this very deep Russian novel. I agree that "children" could definitely be a very simple theme in The Brothers Karamazov by Fyodor Dostoevsky, especially when considering the family of Fyodor Karamazov (who, of course, is murdered). Even the title lends itself to this simple theme in labeling the sibling relationship immediately.
The original children involved here are, in fact, these brothers of the Karamazov family: Dmitri Karamazov, Ivan Karamazov, and Alyosha Karamazov. The Brothers Karamazov by Fyodor Dostoevsky focuses on the differences between children in the same family and, specifically, the differences between the three brothers. Each of the three boys has one trait in their personality that hovers over the others. In other words, each child has one personality trait that is dominant.
For example, the first-born, Dmitri (who is often given the nickname of Mitya), is labeled by eNotes to have "broad passions." This simply means that Dmitri is very excitable with strong feelings and impulsiveness that makes him be quick to action on any of his passions (whether it be love or antagonism).
The second child in The Brothers Karamazov by Fyodor Dostoevsky, named Ivan, has the opposite trait of the first-born. Ivan, then, is absolutely not excitable. He is cool and aloof, with a tendency towards intellectualism.Finally, there is the baby of the family: Alyosha. Different from the other children, Alyosha has a tendency towards the spiritual.
In conclusion, The Brothers Karamazov by Fyodor Dostoevsky can be labeled with the theme of "children" due to the different personalities of the three brothers. Whether it be passion, intellectualism, or spirituality, children of any family can be vastly different. The Karamazov family is no exception.