I don't think they'll believe that the world is always fair, or that everyone in it is (see dd_b's comment).
There's a lot to be said for people believing that their family will treat them fairly. That Peg's kids know that the people who love them will be fair to them, and listen to them, will do them a lot of good, not least in other relationships, because they'll know that they have the right to expect decent treatment from the people they love, and are involved with.
I also think that people who realize that it's possible for parents and other authority figures to treat them fairly are more likely to treat others fairly.
Re: I don't exactly know how to phrase this
There's a lot to be said for people believing that their family will treat them fairly. That Peg's kids know that the people who love them will be fair to them, and listen to them, will do them a lot of good, not least in other relationships, because they'll know that they have the right to expect decent treatment from the people they love, and are involved with.
I also think that people who realize that it's possible for parents and other authority figures to treat them fairly are more likely to treat others fairly.