Oh yes, there is plenty of irony here in Delta Wedding. Although there are inklings of situational irony (when something happens that is different than what we expect to happen) there are much greater examples of dramatic irony (when we know something that a character doesn't know).
One way dramatic irony is represented is in the character of Robbie Reid Fairchild. She thinks George has chosen his family over Robbie, but we know that George can have loyalty to both. The Fairchild family at the Shellmound plantation is both a proud and an exclusive family. Robbie becomes jealous of this family bonding. Her comments express this:
You're all spoiled, stuck-up family that thinks nobody else is really in the world! But they are!
When George Fairchild (Robbie's husband) chooses to rescue his sister from an oncoming train, Robbie believes George has chosen sister over wife. As a result, Robbie leaves George. We know this because George arrives at Shellmond unaccompanied by Robbie (and only accompanied by the filly that is Delta's wedding gift). It is only when Robbie arrives (later in the novel) that her anger is squelched when she realizes just what we do: that her husband George not only has loyalty to the Fairchild family at Shellmound but also to his wife.
Another aspect of dramatic irony can be found within the character of Laura McRaven. Laura, of course, is our nine-year-old narrator who arrives at Shellmound for Delta's wedding very worried that she won't be accepted by the family because her mother has died.
The Fairchilds’ movements were quick and on the instant, and that made you wonder, are they free? Laura was certain that they were compelled-their favorite word. Flying against the bad things happening, they kissed you in rushes of tenderness. Maybe their delight was part of their beauty, its flicker as it went by, and their kissing of not only you but everybody in the room was a kind of spectacle, an outward thing.
We know that Laura's mother's death won't nix Laura from the Fairchild family. Once a Fairchild, always a Fairchild at Shellmound. This is complicated, of course, when Laura gets the chickenpox right before the wedding and can't be the flower girl. Laura is absolutely devastated, thinking that this is the final straw and she can no longer be part of the family. We know, of course, that this isn't true. Because of Laura's mother's Fairchild connection, Laura will always be a Fairchild. The dramatic irony is presented here mostly in Laura's nine-year-old worries: that a death or a sickness would estrange her from the family. As readers, we never doubt the loyalty of this family, so this is a perfect example of dramatic irony.