The core reason for the Division was
1) the people following the annointed King (David)
2) the king of Israel being put in power by the Army (Ish-boshet- appointed by Abner)
David was the anointed Kind, and the Leaders of Judah accepted him is king (2Sam2vs4).
The Rest of Israel accepted the appointment of Ish-boshet as leader under the appointment of the Abner commander of Saul's Army.(2Sam28) This lasted for two years till Ish-boshet was murdered.
The Bible states that David was King over Judah for 7 yrs and 6months and 33 years over both Israel and Judah. (2 Sam 5vs4)