snbzk, the way you should think of it is like this:
In an adjective clause (the food
that my dad makes), take out the partial sentence (I don't know the correct term) from the clause (that
my dad makes). Any が there can become a の. For example:
父が飲んだビール〜
父の飲んだビール〜
母が作った靴下〜
母の作った靴下〜 (anyone appreciate my unintentional reinforcement of gender roles?
)
I don't know what "following sentence" you're referring to (I'm guessing you forgot to paste a sentence in your post), but that's my explanation of the の／が phenomenon.
Nagoyankee: Would you say that the use of が used to be favored, but as times change, preference for の has grown, and that's why the latter sounds softer than the former?