This question is for my wife whose father's house (where she was born), which is in a city (A) different than the current city where we are presently staying (B). I was born in an altogether different city (C), which I consider as my only hometown in addition to city B.

The question is about my wife's prayers, whether qasr or full, in city A and also city C.  What if my wife has no intentions to settle in city A in future?

If she stayed in city A till she became adult, and still considers it as home, although she do not intend to go back to live there, then her prayers there are full, while if she left it in her childhood, or she does not consider it as home any more, but she goes there just to visit her parents, then her prayers are qasr.
With regard to city C, her prayers are qasr.