(about your latest answer to renly knowing about incest) that doesn’t make sense. Robert was pretty young, so Stannis wouldn’t be an heir for a long time with Margaery becoming new queen. This plan is so much easier than going to war. And why would Stannis hide if Cersei was executed and he didn’t need to fight for throne? Robert would have children with Margaery and Stannis would probably have to go to war with the West. Renly had no reason to hide his knowledge.

I don’t really understand what you’re saying here: you seem to be suggesting that replacing Cersei with Margaery would somehow avoid war, but would involve Stannis going to war with the Lannisters; Cersei being executed but somehow not for incest and adultery.

Let me clarify my previous post:

Renly’s plan doesn’t work if he doesn’t know about the incest. If Cersei is a faithful wife, it doesn’t matter whether Robert sets her aside in favor of Margaery, because Cersei’s children will inherit ahead of Margaery’s children. And if Margaery’s children aren’t going to inherit, Mace Tyrell – who is consistently motivated by a desire to put a Tyrell grandchild on the Iron Throne whether the father is Renly, Joffrey, or Tommen – has no reason to go along with the plan. So Renly had to know, because the plan did go ahead, so he must have persuaded Mace to go along with it, and there’s really only trump card to play in that argument.

To answer your specific points:

While Robert is fairly young, he’s not in great health, and could die at any moment (in part because Cersei is repeatedly trying to assassinate him). But Robert living or dying is only relevant to the Tyrells if he marries Margaery and sires an heir with her. If he doesn’t marry, or marries someone else, they (and Renly) are just as out of power as they would be if he stayed married to Cersei. They only have a motive to reveal the truth if that means that Joffrey, Tommen, and Myrcella are disinherited and Margaery’s children take precedence in the succession, and that scenario requires Robert to agree to marry Margaery first.
Robert replacing Cersei with Margaery doesn’t actually prevent war, as even your scenario points out, because replacing Cersei also means replacing her kids, and Tywin will go to war to uphold their rights to the succession – and if there’s no legal justification for Cersei and her children being set aside (like say incest and adultery), a lot of other people might join Tywin, just like in the Dance of the Dragons.
Stannis left for Dragonstone when Jon Arryn died, before Renly had a chance to put his Margaery plan into effect. Hence why Renly’s only at the stage of showing Margaery’s miniature to Ned to gauge whether he can use the resemblance to Lyanna to entice Robert in Eddard VI, and talking up Margaery to Robert in Eddard VII. He hasn’t yet brought her to court so that Robert can bed her and then marry her by the time that Robert dies. So it’s not possible to “quietly kill Stannis (Tyrell style) if Robert refused to marry,” because Stannis has already taken steps to protect himself.

I’m not sure you already had this question but why did Renly choose to marry Margaery to Robert and not Joffrey? Wouldn’t he get the same advantages without the trouble of removing Cersei?

The point was to remove Cersei.

Cersei was a clear enemy of both Baratheon brothers (and vice versa), as we see from Bran II of AGOT where she talks to Jaime about all her enemies, or from Eddard XIII where Renly urges Ned to launch a coup against her, or from Sansa V of AGOT where Cersei marks down Renly as a traitor well before he declares his candidacy for the Iron Throne.

I’m sure I’ve missed it when I read the books, but why does Renly want to wed Margaery Tyrell to Robert?

Renly wants to wed Margaery Tyrell to Robert as part of a larger plan to oust the Lannisters – get Cersei out as queen, get Joffrey/Tommen/Myrcella out as heirs – and replace them with the Tyrells, with Renly likely becoming the next Hand of the King as the king’s loyal brother, the man responsible for uncovering Lannister treachery, and as a close ally of the Tyrells through Loras.

Renly didn’t know anything about incest. Idk why people seem to think so, but why would he hide it? He’s not that stupid. Robert would marry Margery if he needs Tyrells – and he would need them, their money and their army, if he’s going against Tywin. Renly could’ve gotten what he wanted without doing anything. Hell, it was easier to quietly kill Stannis (Tyrell style) if Robert refused to marry rather than bother fighting a war. No one will fight to put Shireen over Renly on the Iron throne.

I’m not sure how much to put into this response, because I’ve written about this here here here here here, here and here.

But to answer your questions:

Renly hid it, because until Robert signs on the dotted line with Margaery and the Tyrells, revealing the truth would have made Stannis the heir to the Iron Throne. Renly doesn’t want that, nor do the Tyrells.
If you think about it, it’s the exact same reason why Littlefinger and Varys withheld the same information, despite ultimately intending to bring down the Lannister regime.
Rather difficult to do that when Stannis has withdrawn to Dragonstone and started raising an army and navy to protect himself.

Did Renly know about the Stannis/Jon incest investigation/plans? Why didnt Renly bring Stark in on things, since he probably knew and had weeks of time being in the capital with Eddard but does basically nothing till Robert is dead. Or heck why not bring Jon Arryn in on the replace lannisters with tyrells plan?

Renly knew.

Actually, Renly did sort of bring Eddard in on it, rather inadvertently:

Ned was not sure what to make of Renly, with all his friendly ways and easy smiles. A few days past, he had taken Ned aside to show him an exquisite rose gold locklet. Inside was a miniature painted in the vivid Myrish style, of a lovely young girl with doe’s eyes and a cascade of soft brown hair. Renly had seemed anxious to know if the girl reminded him of anyone, and when Ned had no answer but a shrug, he had seemed disappointed. The maid was Loras Tyrell’s sister Margaery, he’d confessed, but there were those who said she looked like Lyanna. “No,” Ned had told him, bemused. Could it be that Lord Renly, who looked so like a young Robert, had conceived a passion for a girl he fancied to be a young Lyanna? That struck him as more than passing queer.

See, here’s the thing about Renly and the investigation: it is not in Renly’s interest for the truth to come out unless and until he’s succeeded in getting Margaery into Robert’s bed. Because if the truth comes out and Robert is unattached, then Stannis becomes the heir to the Iron Throne.

However, if Robert is remarrying to Margaery, then the Tyrells replace the Lannisters in the King’s Landing power structure but because Renly’s brokered the deal and is romantically attached to Loras, they become allies to his faction. And while Stannis might temporarily be the heir to the Iron Throne, the moment that Margaery becomes pregnant, Stannis is out of the picture and Renly’s path to a Handship/Regency is clear.

So what’s happening above is that Renly is both trying to get info as to whether the Margaery as Lyanna 2.0 thing will work but also seeing if he and Ned are sympatico, and neither works. It previews Renly’s pitch to Ned, in that he completely misunderstands how to appeal to Ned and win him over.

As to why not Jon Arryn, well A. Jon Arryn suddenly dying kind of makes that impossible, and B. there’s no reason to assume that Jon Arryn would favor Margaery – he might push for some other marriage.

Why do you say Renly knew about Cersei x Jamie? Doesn’t he just tell Stannis that it’s a good excuse?

Discussed here.

But here’s the short version:

Before he married her, Renly was scheming to get Robert to replace Cersei with Margaery.
Mace and Loras went along with this plan.
None of this actually benefits Renly or the Tyrells unless Cersei’s children could be disinherited as well.
The only way that Renly could promise that to Mace and Loras is if Renly knew about the adultery/incest, which would make Joffrey et al. bastards born of incest.

But, and this is key, the moment Robert dies without having divorced Cersei and disinherited her kids, Renly can’t admit any of this because it makes Stannis the indisputable rightful heir to the Iron Throne.