The sons of Mosiah had been “the very vilest of sinners.” Why such strong language if they had simply ceased to believe what their father and Alma’s father believed? Theirs was not simply the sin of disbelief. So many fall under that condemnation, and do so more than once in their lives. Belief and understanding can change.
What was different for the sons of Mosiah was that they had sought to destroy the church (Mosiah 27:10). Rather than keep their sin as an individual consequence, they attempted to influence others and actively deny the correct doctrine to others. That was the serious aspect of their sin, not simply a lack of belief or faith.
As part of their massive change of heart, they petition their father to allow them to preach to the Lamanites in the land of Nephi. This was the Nephite land of inheritance, and the land from which Alma the elder and the people of Limhi had fled. It was a land where they probably spoke the language, and possibly had some connections that had influenced their previous apostasy.