In my opinion, it is more about semantics than just a case adjustment. The semantics are those of 'inanimate causative action' or 'intermediate action' that require with as a marker of non-animate instrument (cf. written by hand VS written with a pen).
The choice of a preposition, in my opinion, depends on innner semantics of the verb, which historically is close to a meaning of 'making a hap' (as a noun-derived word):
happy <= hap <= happen <= ME happen <= PG hampijaną
In other words, the choice is governed by the semantics of the verb (and not by the complement).
Because parents are 'living beings', but the hap is not, it is not 'feasible' to use 'with', which goes with inanimate 'causative' instruments. And, yes, the causativity for the 'hap' (I'm not sure if causativity is the best term, but let's take this due to the lack of another option) is one of the key concepts here, I suppose.
Because of the causativity, the choice of the 'case-preposition' is governed by the 'hap' and not 'parents'.
In a case of 'being proud', the choice of a 'case' is governed by the 'parents', not 'pride'.