The plan is this:
Zuko knew he had a ticket back home. That was his initial plan, when he first captured Katara. Make sure the Avatar followed all the way home, and let his father take care of the rest.
Unfortunately, or fortunately, which ever side you are on, things changed. Zuko understood the time of the Fire Nation had come to an end, and if his kingdom was to still keep their honor, it was time to fall gracefully. Katara was right when a destiny was to be fulfilled. There was a fairy tale that mothers told their children that foretold the coming of a time where a prince would defy the king. The Fire Nation would fall, but the end of the story was always uncertain. Would the prince be able to bring the kingdom back?
Zuko had no doubt this prophesized prince was him. And he also was certain which ending he would choose.
After much thought, he decided to make it seem he was sticking to his plan to lure the Avatar to the capital. This was his only chance to get back to the capital. He also wanted to release his men from any obligation they had of him. Zuko did not want to bring them into this. Once he was certain the children were taken care of as well, Zuko would face his father.
Assuming the Fire Lord would not attack the Avatar right away, Zuko would take Katara to him. While in the meetings on how best to proceed next, Zuko planned to confront his father. This was the part of the plan he was very uncertain about, and just was going to wing it.
When Zuko was done telling this to Katara, she was amazed.
"But you'll lose your throne!"
Zuko shrugged. "It's a risk for my people. Besides, if I do lose it, my Uncle Iroh will be the next Fire Lord. I am my fathers only child. According to our laws, if all the Fire Lord's heirs have died, or if he has none, than the next living sibling from his father will take the throne. These laws can never be changed." He took Katara's hand. "My throne is of no concern now. What I need you to do is contact the Avatar and tell him what is happening."
"How will I convincehim I'm telling the truth?"
Zuko looked her in the eye. "Tellhimhehas my word, and that the word of a Fire Bender is never forgotten or broken." With that, he leaned forward and kissed her lightly on the forehead. "Can you do this for me?"
She nodded.