Sadly, the marriage between Aerys II Targaryen and his sister, Rhaella, was not as happy; though she turned a blind eye to most of the king's infidelities, the queen did not approve of his "turning my ladies into his whores." (Joanna Lannister was not the first lady to be dismissed abruptly from Her Grace's service, nor was she the last).
The scurrilous rumor that Joanna Lannister gave up her maidenhead to Prince Aerys the night of his father's coronation and enjoyed a brief reign as his paramour after he ascended the Iron Throne can safely be discounted. As Pycelle insists in his letters, Tywin Lannister would scarce have taken his cousin to wife if that had been true, "for he was ever a proud man and not one accustomed to feasting upon another man's leavings." It has been reliably reported, however, that King Aerys took unwonted liberties with Lady Joanna's person during her bedding ceremony, to Tywin's displeasure. Not long thereafter, Queen Rhaella dismissed Joanna Lannister from her service. No reason for this was ever given, but Lady Joanna departed at once for Casterly Rock and seldom visited King's Landing thereafter.
At first His Grace comforted Rhaella in her grief, but over time his compassion turned to suspicion. By 270 AC, he had decided that the queen was being unfaithful to him. "The gods will not suffer a bastard to sit the Iron Throne," he told his small council; none of Rhaella's stillbirths, miscarriages, or dead princes had been his, the king proclaimed. Thereafter, he forbade the queen to leave the confines of Maegor's Holdfast and decreed that two septas would henceforth share her bed every night, "to see that she remains true to her vows."
What Tywin Lannister made of this is not recorded, but in 266 AC, at Casterly Rock, Lady Joanna gave birth to a pair of twins, a girl and a boy, "healthy and beautiful, with hair like beaten gold." This birth only exacerbated the tension between Aerys II Targaryen and his Hand. "I appear to have married the wrong woman," His Grace was reported to have said, when informed of the happy event. Nonetheless, he sent each child its weight in gold as a nameday gift and commanded Tywin to bring them to court when they were old enough to travel. "And bring their mother, too, for it has been too long since I gazed upon that fair face," he insisted.
At the great Anniversary Tourney of 272 AC, held to commemorate Aerys's tenth year upon the Iron Throne, Joanna Lannister brought her six-year-old twins Jaime and Cersei from Casterly Rock to present before the court. The king (very much in his cups) asked her if giving suck to them had "ruined your breasts, which were so high and proud." The question greatly amused Lord Tywin's rivals, who were always pleased to see the Hand slighted or made mock of, but Lady Joanna was humiliated. Tywin Lannister attempted to return his chain of office the next morning, but the king refused to accept his resignation.
-The World of Ice and Fire - The Targaryen Kings: Aerys II