King David, though the best human ruler over God's people, reigned with his own share of family strife and conspiracies that threatened his throne on several occasions. God prophesied he would suffer due to such behavior as punishment for his sins involving Bathsheba and Uriah the Hittite.
Now therefore, the sword shall never depart from your house because you have despised Me and have taken the wife of Uriah the Hittite to be your wife . . .
Behold, I will raise up evil against you out of your own house, and I will take your wives before your eyes and give them to your neighbor . . . (2Samuel 12:10 - 11).
Absalom
David's son Absalom was strikingly handsome with flowing locks of hair (2Samuel 14:25 - 26). Over a period of four years, he quietly gained the trust of the people and won their hearts (2Samuel 15:1 - 7). The next step in his conspiracy to take the throne was lying to his father regarding his purpose in visiting Hebron (verses 7 - 9).
When Absalom arrives in Hebron, where his father was made ruler over Judah and later all Israel, he proclaims himself the new king! His power grab even wins over the support of his father's chief counselor.
And Absalom sent for Ahithophel of Giloh, David's counselor, from his city Giloh, while he offered sacrifices. And the conspiracy was strong, for the people with Absalom grew more and more (2Samuel 15:12).
David learns of the rebellion and flees Jerusalem with many loyal supporters (2Samuel 15:13 - 23). Absalom's army is ultimately crushed by those who still maintain an allegiance to David (2Samuel 18:6 - 7). Absalom himself, while dangling from a tree after his long hair caught its branches, is killed by army commander Joab and his men (verses 9 - 15).
Sheba
Sheba was a troublemaker and rebel from the tribe of Benjamin (2Samuel 20:1). He initiated his revolt after the king had put down the insurrection led by his son Absalom. The revolt, surprisingly, was initially successful, attracting all the tribes except Judah to abandon David. The conspiracy is stopped, however, when Joab pursues Sheba and negotiates with the city of Abel to have him killed (verses 13 - 22).
Adonijah
Adonijah was quite handsome like his half-brother Absalom (1Kings 1:6). While his father David is on his deathbed, he instigates a secret rebellion to have himself become the next ruler instead of Solomon. Needing additional support for his plan, He also convinces army general Joab and one of the two High Priests named Abiathar to support him (verses 5 - 7).
Nathan the prophet and Bathsheba (Solomon's mother), upon learning of the conspiracy, take the bold move of informing David concerning Adonijah's actions.
And she (Bathsheba) said to him, "My lord, you have sworn by the Lord your God to your handmaid, saying, 'Surely your son Solomon shall reign after me, and he shall sit upon my throne.' And now, behold, Adonijah reigns. And now, my lord, you do not know it . . ." (1Kings 1:17, see also verses 22 - 27).
David quickly responds by having Solomon publicly crowned king at the Gihon Spring (1Kings 1:38 - 39). All support for Adonijah and his conspiracy, immediately after Solomon's anointing, crumbles and leaves him begging for mercy (verses 49 - 53).