So I guess the vocative of 'athair' doesn't involve using the 'a' particle?
no. It never does when a word starts with a vowel.
I believe in some texts (when people stick to more conservative orthography) it does appear (and it’d be a athair there), but today it is most often not written before a vowel.
The same happens to the relative particle in dè a tha… vs dè tha….