Some English people pronounce wrath as wroth. I'd say the lyrics have nothing to do with Rothschild whatsoever.

Proof that he sings "Rothschild" instead of "Wrathchild" is obvious from listening to the song.

Lyrics I was born into a scene of angriness and greed, and dominance and persecution. My mother was a queen, my dad I've never seen, I was never meant to be.

Now I spend my time looking all around, For a man that's nowhere to be found. Until I find him I'm never gonna stop searching, I'm gonna find my man, gonna travel around.

'Cause I'm a wrathchild, well I'm a wrathchild. Yeah I'm a wrathchild. I'm coming to get you, oh yeah.