While these events are mostly the same between the films and the books, I'm specifically going to focus on the films as that's what you seem to be focusing on.
The Two TowersThere was never any question that the Rohirrim were powerful enough to save Rohan. The issue from the very beginning was that Théoden had sent them away and they had no army at all. Their return wasn't much of a surprise, either; it was flat out stated Gandalf went out to get them, and the battle in the mean time wasn't about winning, but about surviving until the Rohirrim actually showed up. Combined with the sunlight (which does still give Uruk-hai a distinct combat disadvantage, albeit not to the extent of regular orcs), it's not at all odd that they'd win once the Rohirrim showed up. Sure, the timing made it seem like a deus ex machina, but their return was guaranteed to happen and clearly projected in advance.
Return of the King1. Gondor's army was already in bad shape, due to one strategic disaster after another on Denethor's part. Had the entire army been able to fight at Minas Tirith, they would've won; at full capacity, it was a stronger army than the Rohirrim. Unfortunately, Denethor's squandering of his troops put them at a significant disadvantage. In a misguided attempt to recapture Osgiliath, he had sent a large chunk of Gondor's army on essentially a suicide mission. Osgiliath was already designed for defense, and was heavily reinforced by Mordor in anticipation of this attack. Losses and injuries sustained in this battle—entirely avoidable though they should have been—were key in wrecking Gondor's army just in time for the battle for the Pelenor Fields. Had Denethor been even vaguely competent, or had Aragorn led Gondor's troops from the start, the effort to defend Minas Tirith wouldn't have been nearly the trainwreck that it was. I wouldn't call these soldiers pansies, only Denethor.
2. Though certainly a key component in Gondor's eventual victory at Minas Tirith, the arrival of the Rohirrim was not the turning point. Rather, it was when Aragorn brought the Dead Men of Dunharrow that Gondor effectively won. All of a sudden, Mordor's troops found themselves up against a horde of terrifying and invincible ghosts. Much like the Rohirrim's return in
The Two Towers, this plot thread was brought up well in advance of its payoff, and a good chunk of story was dedicated to making sure it actually happened. A bit of a deus ex machina insofar as they literally could not lose, but not too huge a deal since the reasons for the battle storywise was to allow Aragorn the opportunity to take his place as king of the dead, and to give Merry and Pippin a chance to prove themselves.
My understanding is that the entire plot of the Hobbit and the LOTR books were written from the POV of the hobbits. Hobbits aren't the brightest bunch, so what you see is their rather simple explanations of the events.
This is only partly true. Hobbits live simple lives and have simple desires, but they aren't themselves simple. The books did a
much better job showing this, and it can especially be seen in Merry's use and understanding of maps, or the fact that he knew of the one ring's existence even before there was any indication that it was the same ring Bilbo had.
The story *is* mostly written from their point of view, but it's really Aragorn's story. The hobbits are basically Tidus to Aragorn's Yuna. That said, it can definitely be seen as reliable, at least regarding the things it actually includes. Some important exposition may be limited, but nothing actually in it is inaccurate to what actually happened in-universe.
