Skins are not canon. Corsair Quinn and other skins are sometimes considered mini-canons that are much more open to interpretation than the actual, consistent, wide-ranging canon. The Bilgewater event was part of the main canon. The in-lore happenings tied to the event are totally contained within Burning Tides. Shadow and Fortune, which occurs I think a week after Burning Tides, serves to introduce the relationship between Bilgewater and the Shadow Isles, in addition to serving as a sort of extended epilogue.
Illaoi has already dumped Gangplank well before the events of Burning Tides, implied to be due to his lack of ambition and lack of a willingness to change to what he wanted, contrary to the commandments of Nagakabouros. She still has feelings for him that being why she saves him in The Burden, in between the other two stories. However, she seems to have a pretty good relationship with Miss Fortune, too.
Since you mostly seem to be interested in Gangplank himself, his universe page is here.