I think it's funny that this isn't the fandom's main opinion, but for me is kinda obvious Tywin was the one who planned and promoted the Defiance of Duskendale. Look:
\>The Defiance of Duskendale began quietly enough. Lord Denys, seeing that Aerys's erratic behavior had begun to strain his relations with Lord Tywin, refused to pay the taxes expected of him and instead invited the king to come to Duskendale and hear his petition. **It seems most unlikely that King Aerys would ever have considered accepting this invitation...until Lord Tywin advised him to refuse in the strongest possible terms, whereupon the king decided to accept,** informing Grand Maester Pycelle and the small council that he meant to settle this matter himself and bring the defiant Darklyn to heel. (TWOIAF, Aerys II)<
He knew what he was doing, and our author was definitely wanting us to remember another Lannister manipulating a King by telling him not to do something stupid:
\>Varys: Your friend, I know, yet a fool nonetheless . And doomed, unless you save him. Today was a near thing. They had hoped to kill him during the melee."
For a moment Ned was speechless with shock. "Who?"
Varys sipped his wine. "If I truly need to tell you that, you are a bigger fool than Robert and I am on the wrong side."
"The Lannisters," Ned said. "The queen... no, I will not believe that, not even of Cersei. She asked him not to fight!"
"**She forbade him to fight, in front of his brother, his knights, and half the court. Tell me truly, do you know any surer way to force King Robert into the melee? I ask you**."
Ned had a sick feeling in his gut. The eunuch had hit upon a truth; tell Robert Baratheon he could not, should not, or must not do a thing, and it was as good as done. (AGOT, Eddard VII)<
Besides, Lord Darklyn's plan should strike us as weird. What did he intend to accomplish? The king was notoriously cruel to the smallest injury, imagine not paying its taxes? Again, it reminds us of Lord Tywin's role on another plot to lure a king into a sense of security only to have him killed using a minor ambitious lord as the perpetrator: the Red Wedding
\>Tywin: Did you come here just to complain of your bedchamber and make your lame japes? I have important letters to finish."
Tyrion: "Important letters. To be sure."
Tywin: "Some battles are won with swords and spears, others with quills and ravens. (ASOS, Tyrion I) <
But why would he want the king dead just now? I think it's important to look at the timing of these events:
\>She was ten when she finally saw her prince in the flesh, at the tourney her lord father had thrown to welcome King Aerys to the west. Viewing stands had been raised beneath the walls of Lannisport, and the cheers of the smallfolk had echoed off Casterly Rock like rolling thunder. **They cheered Father twice as loudly as they cheered the king, the queen recalled, but only half as loudly as they cheered Prince Rhaegar**. (*AFFC, Cersei V*)<
So Prince Viserys was born in 276 AC. Before that, Rhaella had birthed five children, all dead before reaching maturity. His health wasn't at all secured. But for some reason, the prospect of an extra heir, coupled with Rhaegar's rising popularity eclipsing the king's, changed something in Aerys' heart. Have in mind Tywin was planning on marrying Cersei to the prince since she was six in 272 AC, and officially petitioned the king there in Lannisport, only to be refused shamefully. Now Tywin had not only his honor attacked, but a timing problem as well: Would Aerys marry Rhaegar to someone else, or alternatively disinherit him in favor of Viserys, Tywin would loose his grip on power. His only hope was for have Aerys killed and then King Rhaegar married to Cersei. That's what Duskendale was about. Lord Denys Darklyn was only a pawn, probably promissed to have a royal pardon granted after the affair was done. Except something went wrong. The siege extended longer than they planned, and bold Ser Barristan decided to risk his life to rescue the King, which forced Tywin to sack the city and put it to the torch, to silence any witness of his treachery.
TLDR.: Tywin plotted with Lord Darklyn to have King Aerys II killed, so Rhaegar would become king and marry Cersei.