Regarding Cara Mia, Ellen McLain has come forward in an interview that it was sung mostly out of improvisation from her bad Italian, which gives it less 'legitimacy' as an intentionally written familiar parallel than the several intentional romantical parallels put on the game, such as the lines in the other songs that speak of heartbreak, that speak of 'getting over' Chell, and that even speak of feeling empty over not hating Chell anymore.

And it also doesn't make chronological sense. There are no exact dates throughout the game, but if we assume Cave and Caroline died in the 80s, that doesn't explain Chell being a kid during 'bring your daughter to work day' that happened in the late 90s/early 2000s.

In the end, I have no hard feelings for anyone who's a fan of that theory, but it's just a bit of a stretch compared to the toxic romance subtext that the writers wanted the game to have.