The "slower" approach they've obviously decided to take with Tywin/Jaime suggests strongly they intend to milk this family aspect of the story for all it's worth. Already they're humiliating and isolating Jaime psychologically, with Brienne, Cirsei, Tywin and Joffrey all displeased or loathing him, turning him in the Lannisters' eyes into a second Tyrion, basically, which should in turn bring Jaime and Tyrion closer. As we know, in the end Brienne will also have her way.

For me that heralds a season of mostly "psychological development" and "change of perspective from the audience" for Jaime, which means he will mostly have to interact with others in KL, and transform himself through the events. He will side with Tyrion, send Brienne on her quest, confront Tywin, probably turn the page with Cirsei in the end (or they'll set it up so it happens early in season 5).

TV viewers still see him mostly as a villain, while Cirsei oscillates between somewhat a victim and mostly a villain(while Tyrion has a little too much audience sympathy, but it's hard to help that). IMO this season is when the writers will try to turn that around, and as they don't have the means of GRRM to achieve any of this via Jaime's POV, they brought Jaime to KL's early, where they can show him interacting with Tywin, Cirsei, Tyrion instead and be a more integral part of how things will go down. His relationship with Cirsei is already sourer than in the books, more obviously she's "Tyrionized" him already, and so did his father. But I suspect she in a good part was venting anger and frustration, kind of to have him crawl back in guilt to her with apologies rather then truly rejecting him. But she will pay for that down the line. We'll see where grief will lead her... Personally I would not be surprised if after Joffrey's death she changes her mind, they seek one another for comfort and apparently make up, and she desperately want Jaime to protect Tommen, thus ending up standing against Tywin's wishes for Jaime, but this will go south over notably Tyrion, and the changes in Jaime. When she finally wants him by her side, I guess it's likely it will be Jaime's turn to tell her back "it's too late".

What's also clear, though I saw it infuriated many readers to see Tywin react "too calmy" to Jaime's opposition to his wishes in episode 1 compared to how it went down in the books, is that they plan to have the father-son relationship deteriorate on screen instead (again, because they don't have POVs to achieve this, they need to show it. Tywin would have looked a fool, not shrewd, had he right away exploded at Jaime at this point). For now Tywin wasn't "too calm" but clearly bitterly angry yet bidding his time, swallowing his anger with Jaime, probably certain he will in the end have his way with him. But of course he won't.

There's many ways this could go from there. Will Tywin try to have Joffrey throw Jaime out of the KG, only to make it sound too much like an order and see Joffrey peevishly refuse his request merely to show Tywin who's the King? (Joffrey likely would prefer to have Jaime close to further humiliate him anyway.). I'm guessing Tywin's "olive branch" is extended to Joffrey, anyway (might be a reference to the second sword, offered as gift prior to the wedding). I guess this could happen, as another big confrontation between those two, maybe ending in veiled threats, would provide a good motive for Tywin to appear to want Joffrey dead. It will depend how long they intend to wait before revealing who killed Joffrey. Will LF await Sansa on the ship, or will they wait to reveal who saved her when she reaches the Vale or Eyrie (showing Dontos being killed, but without her knowing?), meanwhile leaving the audience to guess for an episode or two who used Dontos? They gave a big clue last year with LF's direct attempt that Sansa refused, but LF is no longer around to remind the audience of that detail.

Their general plan seems obvious. By the end of this season, Jaime has to be seen in a much more sympathetic light, which they'll achieve by making him the punching bag of Tywin and the ally of Tyrion against the rest of the family, as well as with his transformation with notably his decision for Brienne (which is around ep. 4, IIRC). To replace Joffrey Tywin is being established as the central villain in full swing, to be killed at the end of the season and replaced by Cirsei in that role, to an extent as she rather loses it in the vein of Joffrey. Cirsei and Margaery both have to be gradually built up to take the center stage in KL next season (though KL events shouldn't be as central or prominent to the series in season 5, I still doubt they will deprive the audience too much of "Cirsei's downfall".