She is not delusional...well maybe she is, but that will come up if and when she ever reaches Westeros and really thinks she can burn all of the families who betrayed the Mad King.
She is delusional and it's already come up.
Honestly [blackout]She has made fewer mistakes than Joffrey, Robb or Stannis up to ADWD and yes, her desire to do the right thing is a bit naive. But she is learning on the job and I can promise will either come back as a better Queen or as a tyrant in the next book. Either it should be fun to watch.[/blackout]
I wouldn't say she's made fewer mistakes, only that she's had to pay less for them.
He does say "destroy my brother's army." But in the book:
Don't kill Stannis.
In the show:
After I win, I'll team with Robb Stark (along with my men from Storm End and the Tyrells) in killing Joffrey.
Why would people ever be on his side?
Renly is incredibly inconsistent between the show and book, almost to the point of being two separate characters who happen to share the same name. In the book, he didn't want Stannis dead but had no interest in helping Robb and was going to make Catelyn watch his army defeat Stannis to prove the point.
They're only on his side because the Tyrells used him as a power grab and they had the largest army to back him.
Also, I never understand this traitor business. Robert was a traitor; Ned was a traitor; Stannis WAS a traitor during Robert's Rebellion. Power resides where people believes it resides. The truth is very few will ever believe it resides in Stannis, because it is clear all his power lies in the Red Witch. One day, he will lose his usefulness to her. On that day, he leaves the story.
The circumstances of Robert's Rebellion and the War of the Five Kings are completely different. Rhaegar "kidnapped" Lyanna. Brandon Stark went to King's Landing and threatened to kill Rhaegar to get Lyanna back, he was arrested. Rickard Stark went to King's Landing to get him and entered a Trial by Combat, where he was burned by King Aerys ("fire is the champion of House Targaryen") and Brandon choked himself to death while watching. Aerys then commanded Jon Arryn to turn over Robert and Ned to be executed for no legitimate reason (especially Robert). He said no and the Baratheons, Arryns, Starks, and Tullys (after marriages) declared war. Aerys was already becoming increasingly unpopular, even Rhaegar saw this and knew there needed to be changes.
With the War of the Five Kings, Robert dies and 3 men claim the throne. Of those 3, Renly has the weakest claim (i.e. none). He does it simply because he knows he's more popular than Stannis and can have his boyfriend's father support him. He thinks that's enough to win the throne and be a good king, when he's just naive and, in reality, a pawn for the Tyrells.