The Run DMC lyric actually sounds like the (previously unmerged) father vowel /ɑ/ went toward the bother vowel /ɒ/ than the other way around. I might even put it as /ɔ/ or /o/ when listening to the sounds on the IPA chart.

Whereas if you listen to the pronunciations on Merriam Webster father and bother it actually lists them both as /ä/, which is apparently a near-back vowel instead of back. I don't know which one NY does though.