While there are a lot of well-known bad dads I'm gonna go for a few more obscure ones.

Ushiromiya Kinzou from Umineko no Naku Koro ni is a smörgåsbord of dysfunctional traits. Manically interested in the occult, unpredictably moody, obsessed with a mysterious woman who may or may not actually be there, and with a penchant for playing cruel mind games on his extended family, particularly his children. To say that Kinzou is difficult for his family to handle is an understatement. What's worse is he's the pivot that the entire plots revolves around, so you can bet things go absolutely pear-shaped many times over before all is said and done.

From the exact same story we also have Rudolf Ushiromiya, one of Kinzo's sons and the father of the main protag Battler. Rudolf is a flaky dad at best who earns his living doing various shady activities together with his mysterious girlfriend Kyrie. Though his family (and his son) despise him for his lifestyle he couldn't care less. He will occasionally make token efforts to be a father but they never really amount to anything and he always falls back into being an uncaring jerk towards his son. A pretty cut-and-dry poopoodoodoo dad.

What's there to say about lord Daigo from Dororo? He decides that the only way to pull his domain out of a death spiral of sickness and famine is to make a deal with some demons and pay them with every body part of his unborn son that's not strictly vital for life, leaving the baby as barely living blob of meat. Then, despite his wife still showing affection for the mutilated child, Daigo goes "Yeah nah, chuck that thing in the river.". He might be acting for the good of his people, but he sure as FUCK isn't acting for the good of his son and wife.
/Crooh