I know quite a number of songs about family but most of them are Japanese songs. xD Got a few in english that come from my charries' theme songs though :Pnot sure if you're looking for the happy kind or the sad kind xD overall they're still about family.
There's Saihate or also known as The Furthest Ends, which is about a kid missing her parents because of a divorce, and she just wants to know how they're doing. It's a beautiful song and I love Mero's version of the english one xD
Another is Ayano's Theory of Happiness, which is more about sibling love, ;w; there's an English version to it somewhere on youtube! ^^
Yellowcard's latest albums have a song called 'Ten', which is really stunning! I'll let you listen to what's it about
Boyce Avenue have a bunch of amazing music and songs too! But 'Broken Angel' is the one that's really about family I guess
(about a father and daughter)
there, you now know the music I listen to. x'D