True, God had predestined Rehoboam to an immediate failure as king. Due to Solomon's idolatry, his son Rehoboam had NO chance to lead the whole nation. But even though God had already decided to take most of the kingdom from Rehoboam, the king had his own responsibility in the matter too. Here is how it happened.
When Rehoboam became king, the people approached him requesting some relief from the heavy-handed taxation to which his father had resorted. Rehoboam's first advice came from elderly men who knew what they were talking about. They told the young king to relax the vise grip that had been used to oppress Israel in the later days of Solomon. Regrettably, Rehoboam ignored the good counsel of the aged and sought for the opinions of men from his own generation. They were foolish and inexperienced. They led him down a ridiculously fruitless path. They advised Rehoboam to tell the nation, "My little finger shall be thicker than my father's thighs." Needless to say, that speech didn't go over so well. Rehoboam lost most of his followers that very day.