Dany marries Daario in season 4. Yuck, I know, but if Dany is going to Dorne, Hizdahr zo Loraq will be out of the picture, and Dany needs to be married before Quentyn enters the picture.
Dany dismisses Jorah as a traitor, like in the book.
The whole subplot of Arianne Martell trying to crown Myrcella is dumped entirely, along with Aerys Oakheart and Darkstar.
Dany and her army sail for Dorne at the beginning of season 5.
Varys and Tyrion sail to Pentos after Tyrion escapes the Black Cells and murders Tywin. They are greeted by Illyrio Mopatis, who has hired an army of sellswords, the Golden Company. Among the sellswords is the young warrior Griff and Jorah Mormont. TV viewers will assume Varys and Illyrio and the Golden Company intend to support Dany.
Tyrion begins to get suspicious that Griff is more than a simple sellsword. They run into some trouble on their voyage (pirates maybe), and when Griff is placed in danger, some of the others show an unusual level of concern for his welfare. Tyrion saves his life.
Dany arrives in Sunspear asking for Doran Martell's support. Griff also goes to Dorne, revealing his undyed platinum hair and claiming to be Aegon VI. Both groups encamp around Sunspear, but aren't in open conflict, both hoping to secure an alliance with Dorne.
Dany's dragons are becoming massive and uncontrollable and are confined to the dungeons of Sunspear, but not before Drogon escapes.
Quentyn Martell attempts to woo Dany away from Daario, but she is unimpressed and unreceptive.
Jorah kidnaps Tyrion and escapes Aegon's camp, hoping by bringing him to Dany he can return to her good graces.
At a melee, Drogon returns, kills both knights and eats them. Soldiers attack Drogon, but Dany tames him with a whip and flies off and disappears.
Quentyn sees that he has lost and Aegon will seal an alliance with his father by marrying his sister Arianne. In a desperate attempt to reverse the situation he sneaks into the dungeons and attempts to tame a dragon like Dany, wins a Darwin Award and gets himself roasted for his trouble. The dragons escape.