As long as she has her PSN account on the PS4, it should save her progress. Though I do hear that people have to keep re-assigning skills since they appear as if everything is newly unlocked every time you start a game.
Yeah, that's totally annoying. I hope they fix that in the next patch.
Anyway, the wife shouldn't even need a PSN account. As long as she has a local profile on the PS4, it should save her progress to that. The only thing I can suggest is making her character initially with her having launched the game. Then quit out, relaunch as you, and have her join.
My GF's local progress is always saved apart from the aforementioned "new skills" bug but we also imported from the PS3 version, so I did launch the game as her to do her import before we tried playing together. Maybe local co-op uses the other player's local save if it already exists, but it won't actually
create one. /shrug