In some traditional Christian beliefs, there is an afterlife. Bad people go to a place called "hell," ruled by an evil spirit called "the Devil" or "Satan," and suffer forever. Good people go to "heaven" and are united with God.
"The children were full of hell" is a strong way of saying that the children were mischievous and behaved badly. It is a joking reference to the idea that the children might be in the control of evil spirits. Other similar English idioms include "The children were full of the devil today," "I don't know what's gotten into you," "I can't imagine what possessed you to do such a thing." Young adults getting drunk and behaving badly are said to be "raising hell."
"Hell" used to be considered a "bad word," even into the 1950s, and people sometimes said "heck" as a substitute. Even now, to say "the children were full of hell" means they were really bad. An elementary school teacher would never say "my kids were full of hell today;" she would more likely say something like "my kids were very challenging today."