It's not a matter of "short attention span". It's a wholly different medium of storytelling, with its own conventions and limitations which are very different from what's possible to do in large books.

It's not that the Dorne stuff was bad (though I found some Ariane chapters frustrating because she wasn't the character I wished to read about), but it's a wholly new story arc in a series that already has many, more than the average TV series, even for historical drama. It will be a challenge to include it in way faithful to the books. The other main arcs had time to grow over 3 seasons (plus one to come), adding characters in the ongoing flow but rarely starting new arcs without at least an established player to hold the fort (Tyrion with Tywin, then Arya etc.), leaving time to the viewers to get interested. Introducing a whole new arc with completely new players changes a lot the nature and pacing of the storytelling. The Dorne storyline will have to start slow (while the other arcs can move on faster), give time to present properly all the players before the story really starts, without familiar faces to ease that part (the only thread connecting them to rest is Oberyn). But at the same time it will have to hook the viewers fast or those scenes will rapidly become the "boring ones", and this will be further complicated by the fact for the main players it happens at a time when things slow down (some have very few chapters/episodes). It's not impossible to do that, but it's risky... if Ariane and Doran don't hold the interest of viewers very fast, their scenes will just frustrate viewers who'd rather see the story of the characters they already like. A few shows have tried to introduce a new "main arc" midway and lost a many viewers for it. It will also be expensive, as all the other arcs remain active, with their full share of locations and their full cast - so it's a real expansion budget wise.

In the books it's different. Cost is not an issue, you can give the readers as many details to follow as you wish, you can even devote as many scenes as you feel it's needed to build interest. This came at a point where the readers were anticipating the involvement of Dorne and knew quite a bit of its back story etc. Martin could afford to give them a full introduction and slowly build interest before he started revealing how it fitted with the rest. I doubt the TV shows will have enough screen time to devote to Ariane and Doran, at the expense of all the rest, to really make it work as a "main arc", but a shortened introductory arc as they gave the Greyjoys in s2 would work.

I'm not saying they'll cut completely the Dornish subplots (which are a setup for what's to come in WOW) nor even the plot points they're involved in (they need all the realms involved...), but I wouldn't be surprised that they choose to limit what's shown from it to what they really need and delay their full arrival as main players in the story until WoW events and when the characters are a bit familiar. First we'll see the Dornish in KL next season, with the death of Oberyn and the introduction to their back story as allies of the Targaryens. During the AFFC/ADWD episodes, we will probably have Quentyn as it concludes with Dany and his death (it's not events they'll want to cut from Dany's arc). We will probably have Aegon's arrival, and what I suspect is that they may wait until the sending of Ariane Martell to Aegon to make contact and gather intelligence so Doran can make his mind about him (early in AWOW) to have the Dornish become more important players. What they might cut or seriously shorten (as in "have a lot happen off-screen" is most of Ariane's back story with the Sandsnakes's "rebellion" and Doran in AFFC. They could use a few "small scale" scenes with Doran and Ariane very sparingly, mostly as plot devices to increase suspense regarding Myrcella's fate after Cersei's arrest and to introduce the notion Quentyn is on a mysterious venture. Ariane wishes revenge for Oberyn but Doran stops it immediately by arresting her (they could have her plot with the Sandsnakes to kidnap Myrcella and fail, and have her put under house arrest immediately, cutting the escape and the rebellion), Myrcella is only briefly re introduced to remind the viewers Cersei's daughter is hostage in Dorne. Then the focus is on Quentyn, and toward the end of the season (as a prelude to Quentyn's death in the season finale) Doran returns and he releases Ariane and explains his plans to her - revealing to the viewers they're fully on the side of the Targaryens... Ariane is confirmed as heir to Sunspear. Then it's the Quentyn BBQ. Doran's next move is to send her as his emissary to Aegon, so it's the time for Ariane to play a larger role. In short, the main plot points are introduced and the characters that serve them are introduced, but not given full player status eating up much screen time to get into Ariane's actions to get Myrcella named Queen and to push aside her father to take his place. It's not the full Ariane arc from the books, not even close, but the main plot points are there and like say, Yara, she'll then be ready for whatever role she goes on playing in WOW.

For Bran and Sam you probably mistook me. I didn't suggest to cut them, I listed them with the arcs I think they ought to continue (with Rickon's, Sansa's etc.), focus on and keep active, filling story gaps if necessary so these characters don't vanish (Bran in particular has few chapters left before WOW and this will have to be fixed, as they did with Theon who was also used as a mean to keep the Iron Islands arc "alive" (and which allowed them to simply bring them back in the finale, tying it with Theon's ordeals and ending it on Yara's cliffhanger). In s4 they'll pass that torch to her at fist. I think they'll modify her arc so instead/beside hunting for Theon she finds herself forced to take command, then she will be forced to leave when she hears, perhaps late, of the Kingsmoot and as she fails with her claim she will return to the North this time on her personal quest to find her brother that will make her a prisoner too. Yara will be the thread that brings the audience through the Kingsmoot arc, before her uncle is established enough to lead his own arc).