Disclaimer: I don't own The Hunger Games and never will. No copyright infringement intended.
The thing is, Katniss Everdeen and Peeta Mellark are broken and they both know it. But it's a little easier since they have each other and the children. Posey and Maverick mean so much to them, and the two have helped erase their parents' scars a little.
But Katniss and Peeta's scars will never truly fade. They've been traumatized forever by the Games and what happened to them afterwards. One or both of them will wake up screaming from nightmares pretty much every night, which sometimes wakes their children. Katniss hates that Posey and Maverick have to hear this and worries that they'll screw the kids up. It's one of the reasons she resisted on having kids for so long, but she doesn't regret them. She and Peeta love them both with every fiber of their being.
Katniss and Peeta have moments where they worry he will snap and go after her again, but those irrational thoughts have gradually faded as the years passed. They don't need to think about it because it's not going to happen.
"You love me. Real or not?" Peeta smiles at his wife.
"Real." Katniss beams back. This is a running inside joke between them now, something no one except themselves and their friends really understood. "Real or not" questions (that Peeta actually has questions about) are now few and far between.
Their lives are not ruined – They've risen from the ashes, so to speak. Future generations have been saved from the horror they experienced. For them, the Hunger Games will be nothing but a horrific event they read about in history books.
Katniss and Peeta's love has prevailed, and no one will ever forget their heroic actions.
Honestly, they're glue holding each other together. Nothing will ever be able to come between them again.
Author's Note: I just finished Catching Fire and Mockingjay yesterday, and was thrilled that Peeta/Katniss ended up together in the end. Also, it's my headcanon that they name their daughter Primrose and call her Posey. As a side, hilarious note, I used a name generator for the son and two different ones gave me "Joshua" first. Almost used it too. Anyway, I hope you enjoyed!