I forgot that padre has more than one meaning until the Word of the Day reminded me.
padre, adjective: tremendous; terrible
Apart from referring to fathers, you may hear padre used in informal language to emphasize a noun.
Okay, this makes a snippet I heard on the bus the other day make a little more sense to me. The woman sitting in front of me was telling her companion about una pelea padre. At first I thought she was talking about a fight with her parents, but that didn’t make sense.
Yes, I know, eavesdropping is bad. But conversations on public transportation are hard to keep private.