Saul started out great, but because of unconfessed sin and pride in his heart, he ended up a madman who committed suicide.
David saw God's hand in his life from the time he was young while he was tending sheep. It gave him confidence to kill a giant. But he sins and commits murder. He confesses his sin and has a right relationship with the Lord, but the consequences of his actions lead to many family problems.
Solomon asks God for an understanding heart. He had listened to his father's charge to him and it seems took it to heart. He did well in the beginning and God allowed him to build the temple. But he took foreign wives to marry and built for them altars and temples to worship their own gods. This caused a downward spin that Solomon never was able to fully pull out of. He probably wrote Proverbs early in life and Ecclesiastes is a testament to a life that is not closely in tune with God. He ended up having the kingdom split in two after him and here is where the kingdom divides. It divides after Solomon's death.
Then they were captured at different times. Israel sooner, they had no good kings. Judah later by Babylon - they had a few good kings. Below is a timeline showing approximate years.
Keep pressing on,
Steph