Do you think there’s any possibility that, instead of marrying Margaery as Renly and the Tyrells hoped would happen, Robert doesn’t remarry & legitimizes Edric instead? He’s acknowledged, most likely being given a good education at Storm’s End, & noble on both sides. Robert tells us he didn’t want to marry after Lyanna died, and I doubt the disaster with Cersei will make him up for trying again. This time, though, he has a potential out. He could marry Edric to Marg even given canon Marg/Tommen.

He’d probably legitimate Edric anyway, since he needs a standby heir sharpish. But no, Robert’s into Margaery:

“Have you seen Mace Tyrell’s boy? The Knight of Flowers, they call him. Now there’s a son any man would be proud to own to…Renly says he has this sister, a maid of fourteen, lovely as a dawn…” (Eddard VII, AGOT)

So I think Robert’s reaction to the news about Cersei is, “I knew she was the wrong woman to marry, let me soothe my wounded pride in Margaery Tyrell.” And Margaery would have played it perfectly, praising his virility to the skies, reassuring him that he’s all man and Cersei a freak of nature not to want him. Given his prowess with bastards, I don’t think children would have been a difficulty. The main question is whether Margaery can inspire him to get himself back in shape so he ekes out ten more years, or whether the exertion of a new marriage causes him to die le grand mort, as it were.