I believe that the mistress (though she existed in real life) was included to contrast with (and give emphasis to) Eva's manipulative/forceful personality. Whereas Eva is resolute, the mistress is passive.
I, for one, like the Big Apple reference. As others have pointed out, the initials B.A. stand for Big Apple/Buenos Aires (in fact, the city is sometimes referred to by its initials, not unlike L.A.). Also, "be a" in that line is a clever play on words. Though I have to agree with Eric, I had no idea what was being said/sung when I first watched it.
Salve, Regina, Mater misericordiae
Vita, dulcedo, et spes nostra
Salve, Salve Regina
Ad te clamamus exsules filii Eva
Ad te suspiramus, gementes et flentes
O clemens O pia