Correction: Stannis does not dislike women, he is
uncomfortable next to women.
He makes some comments that may come off as misogynist, but on the whole they are tame compared to the likes of Randyl Tarly.
No. He has, in fact, ordered Justin Massey (a knight in his service) to use the money from the Iron Bank to hire a sellsword army and seat her on the throne even if Stannis should die in the battle for Winterfell.
Yeah, that's the other part that makes it difficult to see Stannis burning Shireen in the books.
Unlike the show, book Stannis left Shireen and his wife in Castle Black with several dozen knights and Melisandre. We do not get to see his battle with Ramsay and Roose, but we see the terrible conditions, the starvation and blizzard. We see Jon recieve a letter from Ramsay (known as the Pink Letter due to it being sealed in what appears to be blood), telling him of Stannis's defeat and death. At this point, Shireen is still alive and well. Jon declares his intent to desert the Night's Watch and take whatever Wildlings who would follow him to make battle, but as soon as he leaves the hall he is stabbed by Bowen Marsh and the other Night's Watch officers. Thorne is not there, and the treason is much better handled as we see Jon for several chapters fucking up his relationship with his officers, letting his idealism get in the way and ignoring practical advice because it does not match his views (the Hardhome expedition is a disaster, costing the NW their few remaining ships and saving no Wildlings, for example). This is the end of our POV in Castle Black.
As such, the only things we can tell about the future are based on fan theories and some deduction: Stannis is presumed dead. Jon is dead or dying. Ramsay is presumed in control of Winterfell. Clearly, this can't be how it ends.
Stannis was assumed by many to kill Shireen, as a logical conclusion to his story arc, with the theme of sacrifice and misinterperted prophecies being strong motifs of his arc. The problem, then, is how can he possibly kill Shireen when he is hundreds of miles away, locked in mortal combat against a foe in a heavily fortified position and with a blizzard around him, without Melsiandre to do anything about the weather? Stannis must either win, or lose but survive. If he wins, he has no need to kill Shireen yet, but even if he loses, it will take time for him to reach Castle Black. His travel from Castle Black to Winterfell was not in a straight line, due to recruiting the Mountain Clans, but even if he took a direct path immidietly it would still be more than a month. Ramsay's letter was written after he supposedly killed Stannis at the end of a 7-day battle. From what we see, there's little reason to believe any battle between the sides could drag that long, but since it arrived by raven, it would have reached way faster than Stannis could arrive through a blizzard.
The situation at the Wall, meanwhile, will be chaos. Val, the sister of Mance Rayder's wife, is a prominent leader of the Wildlings (Stannis mistakenly treats her as a "Wildling princess", which Jon keeps pointing out is wrong, but despite Martin's best efforts to portray that, that's pretty much how the Wildlings treat her). She has explicitly voiced her belief that Shireen should be killed and burned, for the Wildlings fear Greyscale even in children (measters, who have far more experience and reliable information claim Greyscale is no longer dangerous in children who survive it, but ignorant Wildlings think otherwise. Given the wank they and First Men in general recieve, it would not surprise me if Shireen indeed does become infectious for some bizzare reason, but the Wildlings believe she should die regardless). The Wildlings are by far the most powerful group in Castle Black at the time, and their loyalty to Jon is such that many fans expect them to slaughter the traitors among the Night's Watch, and then turn on Selyse and Stannis's few remaining knights, killing Shireen in the process.
The other option is of course for Melisandre to sacrifice Shireen to resurrect Stannis or Jon (with the assumption that Jon will be revived regardless). Melisandre was surprised by the news of Stannis's defeat, as she could not see him in her flames since leaving Castle Black. Whenever she asked the flames to show her Rh'llor's champion, all she could see was "Snow" (capital S in original text, implying she saw Jon rather than the literal blizzard). In either case, Stannis will have no control over what happens to Shireen.
As such, even if Martin intended for Stannis to kill Shireen originally, at the current state of the books it is impossible. Even if Stannis wins the Battle of Ice (both the battle of Winterfell and the battle around Meereen happen at the same time, nicknamed the Battle of Ice and Battle of Fire), as many fans theories expect (based on some clues in the latest gift chapter of The Winds of Winter, Stannis is aware of the Karstarks betraying him and it hints he is planning his own version of the
Battle on the Ice - Wikipedia), he would need to arrive back in Castle Black before Shireen is killed by either Wildlings or Melisandre. Due to clear issues of timeline, it is extremely doubtful she would survive long enough for him to arrive and sacrifice her.
