Ptolemy VI Philometor was Ptolemy V's eldest son. He is the legitimate heir. Now he is the acting king though he's only a child.
His mother, Cleopatra I, acted as his regent but died after 4 or 5 years. Thus two greedy officials, Eulaeus and Lenaeus declared themselves as his guardians.

Ptolemy VI

Philometor married his sister Cleopatra II. His guardians, foolishly, launched an incompetent war against Antiochus IV, the Syrian king. Their army were defeated and Philometor was captured by Antiochus in 170 BC.
The Egyptians thus realized the vacuum in the throne and declared Philometor's brother, Ptolemy VIII Euergetes II, as the incumbent king. They also declared Cleopatra II, Euergetes's sister and sister in law (at the same time), as the queen.
Ptolemy VIII was cruel to the people and intolerant. This incited the people to demand Philometor's return.

Rome, now having the upper hand, finally intervened and the two brothers agreed to split the Egyptian kingdom between them: Philometor ruled Egypt and Euergetes ruled Cyrenaica (part of the Egyptian empire at that time).
Philometor ruled afterwards for prosperous quarter century. He died in a battle with Syria on a campaign intended to support his daughter Cleopatra Thea there. Philometor left a legitimate heir called Ptolemy VII Philopator.

The new king ruled under the regency of his mother Cleopatra II.
But his uncle, Euergetes, coveted Egypt's throne, particularly after the death of his brother. Euergetes married his sister, Cleopatra II, Philopator's mother, and had Philopator killed right after the wedding.
Consequently, Euergetes became the sole monarch of Egypt in 145 BC. He then ruled until his death in 116 BC. He married his niece, by his sister-wife Cleopatra II, also called Cleopatra III.

From Cleopatra II, Euergetes begot a son called Memphites, and from Cleopatra III he begot two sons who will rule simultaneously after him; Ptolemy IX Soter II and Ptolemy X Alexander.
Resentment rose against Euergetes due to his extreme cruelty so he had to flee Egypt to Cyprus taking Cleopatra III with him and his 3 sons.
In his absence Cleopatra II declared herself as the sole ruler of Egypt. Seeking revenge, Euergetes killed his own son Memphites and sent his corpse to Cleopatra II in Egypt.

Euergetes became powerful enough to invade Egypt. So he successfully retook the throne and Cleopatra had to flee to Syria.
Euergetes died in 116 BC, leaving his wife Cleopatra as the ruler of Egypt with whoever she chooses from her sons.