Starting from the top...
Honestly, one of the things about this update that I found hard to swallow was Garlan having a hate-on for Stannis and Richard Horpe.
... He does? I don't think I ever really indicated such. I mean, he no doubts has a massive issue with Horpe on account of his killing Loras, but Stannis? I don't recall Garlan castigating the man in a non-public, non-political setting.
Garlan is a knight, one who stands out in the series for being one of Westeros' few decent guys; he'd know the score. Renly and Loras were soldiers who were trying to kill Stannis and his men in battle. Turns out one of Stannis' men didn't meekly lie down and die (who'd have thought!), and killed them first.
And Garlan made no bones about that. Instead he made comment on Stannis's conduct following the battle in such a way to deliver a statement to those present, and was made known just who exactly killed his brother.
You might consider it teling that as soon as Garlan start's discussing how miserly and stern Stannis is and how he is totally not going to be cool with any present, Alester Florent (Stannis's goodfather) gets right in there and saying "Guys, no. Don't believe this fucker. Look at the shit his family got us in."
You're mistaking the trees for the forest, I fear. Just because Garlan has a good heart, doesn't mean he's spineless or politically naive. He is after all suspected to play a part in Joffrey's death in canon, by chatting to Sansa long enough to be close to Joffrey and drop the crystal that his grandmother seemed to have lifted from her headpiece.
I just wouldn't expect a fighting man known as 'the Gallant' to take the fortunes of war so personally here when there's little (by feudal standards) cause for it.
The nickname was given to him by Willas as a child, as a way to avoid ridicule as their grand-uncle suffered. There's no indication besides skill that Garlan ever particularly cared for battles and tourneys, which is reflected in Loras being the more famed brother.
Given that, Alester Florent's words and continued insults just seem... out of place. Like an attempt to railroad the scene into conflict. Even if he's so stupid as to try and create conflict between the two factions at a negotiation, someone else from Stannis' side should have been quick to silence him.
Alester Florent is the same man who went over to Stannsi Baratheon following Renly's death and converted to the Red God post-haste, to the point that OTL Courtnay Penrose outright shamed him for it. He's also the same man who tried to bend the knee after Blackwater to win back his keep. Being bold and looking beyond his station are key character points, but your mistake is ignoring the greater setting at play. Both Garlan and Alester are making a play for the banners, with Catelyn Tully as a piece. Garlan focused more on Stannis, while Alester focused more on Mace with each hoping to strike a certain chord. Garlan went for chivalry and greed, while Alester tried to arouse an anti-Tyrell sentiment through honour and war-weariness.
If even a third of the Reach present went over to Stannis, then the Tyrells are walking a tightrope at Bitterbridge, especially considering that many of their key allies are now prisoners by Stannis (Fossoways, Cranes, etc...) and others (Hightowers, Redwyne) aren't even present. Currently the man of the hour is Randyll Tarly, who has the gravitas and persona and prestige at this moment in time to play the peacemaker, but Garlan isn't an idiot who ignores blood relations. Randyll Tarly's children are half-Florent, and he shares a good-father with Stannis Baratheon. Even if Tarly is letting play things out, he's not a man to be trusted.
And so Garlan needs to win back the banners, while Alester needs to take them away.
It's just that he goes a little too far to do it, and Garlan's restraint crumbles in the way of significant stress, grief and
that fucking Florent bastard mud-sling my dead brother-
Ahem.
And so he acts, rashly and unwisely.
What I found interesting however, is that very few comments have looked at the third man in the room, aka Randyll Tarly.
I always found it a bit problematic that a warrior lord with notable ambitions in canon sided with Mace rather than his own in-laws. Granted the Florents are a pain in canon, but it was Tarly that held together matters at Bitterbridge in canon, capturing Stannis's emissaries and putitng the hurt on the foot left behind by the Reach and Stormlander men who went over to Stannis. I mean, if Stannis had won, then he'd be good-brother to the king himself. If Joffrey won... yay, he's served the Tyrells well?
Something to consider.
Another thing to consider is the fact that Petyr Baelish didn't make an appearance at all in the chapter except to confirm he was there.
Frankly, this is stupid too. It annoys me that the Florents seem to be portrayed as petty, incompetent and otherwise unlikable as a whole whenever they seem to come up in the series. The Florents being greedy, stupid, antagonistic arseholes all the time gets on my tits whenever I read the books, because it's the low-hanging fruit of creating tension and conflict.
I suppose the difference is that I don't think the Florents have been portrayed as petty, incomptenent or unlikable completely thus far. You might say that because we as readers and viewers might have had a stronger attachment to the Tyrells (after the Starks they're the closest things we have to a heroic family), but you're ignoring the in-game reality if you do.
The Tyrells aren't loved by all, and certainly not feared or followed like the Lannisters or Starks might. Time and time again we are told of instances where there are other families with better claims to Highgarden, where there are other families with great military strength, where there are other lords in the Reach who are more feared or respected than Mace Tyrell. We are shown instances of the Tyrells trying to gain more prestige and power, instances where the Tyrells try to leverage their advantages into net positives. We don't say much about it because they do it against the Lannisters, but there was a reason a great part of Stannis's army was made of men who once followed Renly, and there was a reason why not every lord in the Reach raised their banners for Mace and Renly.
House Florent isn't being petty or incompetent or even unlikeable in this chapter. They're presenting an undercurrent to Reach politics boldly in the light, castigating a family of stewards for shaming the honour of bloodlines of chivalry and knighthood, men who have centuries if not millenia of history to call upon. He shames them for providing their men and women into the beds of kings to claim benefit (sound familiar), and makes the implication that they have lead the Reach poorly in this time of crisis.
In a way, you might consider Garlan the Baelor Breakspear of House Tyrell currently. I'm not quite sure what comparison works for Alester Florent quite best, but I suppose you could compare him to Aegor Bittersteel's Bracken grandfather mixed in with a bit of Daemon himself. Seeking advancement and restitution both, as it were.
