In my experience, Princess's dining staff does an exceptional job of accommodating special requests. Usually by the second night of the cruise, I start ordering a custom salad of lettuce, tomatoes, and carrots in place of the salad suggested on the menu and have never been refused. I even watched a tablemate describe how she prepares Caesar salad to a head waiter who subsequntly prepared it to her specification for the whole table throughout the duration of the cruise! Even requests for variations in the preparation of entrees seem to be no problem at all.
As you describe it, your wife's diet sounds like it will be no problem at all, though I do agree with Kuki's suggestion about having your travel agent relay it to Princess in advance. In addition to the nightly menu, Princess offers several standard dishes that are "always available" even when not listed explicitly on the menu (usually on formal nights). The "always available" items include entrees like Black Angus Sirloin (tends to be somewhat fatty, as is typical of Black Angus beef), grilled chicken breast (consistently excellent), and some sort of grilled or broiled fish filet. Also, the pasta(s) of the day are always available with "red" (tomato) sauce even if it does not appear explicitly on the menu. Further, the dining staff are very willing to "mix and match" any combination of vegetables, potato, rice, etc., that are available each evening. Thus, I think that your wife will eat quite well!
I also should mention that the buffet in the Horizon Court has such an extensive selection of items that your wife should have no trouble finding something that she can eat.
Be sure to eat lunch in the pizzeria at least one day. The pizzas are excellent!