Helped, yes. Happier, probably... but it usually means something more broad than that and it can vary from person to person. The relevant OED definition is:
[with object] Make tidy or put in order again:
'he sat down at his
desk, straightening his things that Lee had moved'
'they are asking for
help in straightening out their lives'
As you can see, the example is very non-specific.
In the context that you've cited "straightening out" could involve, for example:
- Foster children who had become involved in petty crime. Straightening them out could mean getting them back on what is described, not coincidentally, as the "straight and narrow".
- Getting them off substance abuse (though this would be less of an issue with foster children of the ages described in that book).
- Rebuilding their self confidence and belief in themselves after bad experiences in earlier childhood with people who were supposed to care for them.
- Helping them overcome learning difficulties which made them feel alienated from their peers at school.
Basically, anything that improves people's lives and steers them away from self-destructive paths (or lifestyles which are without hope of something better) could be described as "straightening the person out".
A greater amount of happiness is usually the result, but it's more of a by-product of the "straightening" than the actual thing that's changed.
I just noted dukerasputin's comment; he's correct, in some cases "straighten out" can have a negative connotation in the sense of making someone more conservative and conventional, but not always. In the context of that quote I would say that it refers to taking lives that are in some way damaged and unhappy, and restoring them; putting them back on track, as it were.