Dolores's dad is pretty much the source of all her problems. He works for Mrs. Masciotte as a property manager… and he's managing more than her property, if you catch our drift. They have "weekly business" (1.36) together that takes place in private and sometimes lasts for hours.
He yells and screams at Ma when she tells him not to make racial slurs, and when she calls him "an old lady's whore" (2.94), he beats her senseless. Classy guy all around, this dad.
Despite all this, Dolores loves him. Well, love might be too strong a word—she wants attention from him, too. When Ma gets goes away for a week, Dolores couldn't be happier; she gets to spend time with him and only him. They hang out in the pool all day. "He was a flirt" (2.147), Dolores says, and she likes it, a wee bit of an Electra complex going on here.
However, the week with Dad was supposed to be for him to tell her that her parents are getting a divorce. He doesn't tell her, though, and instead just leaves; once he's gone, Dolores hardly ever sees him again. Instead, she resents him forever. He tries to get back into Dolores's life, but she tries her hardest to avoid his calls.
Eventually, he just dies, which Dolores finds out through a letter. She never reconnects with him, or even goes to his funeral. But through therapy, she's able to come to realize that while "he had been a s***ty father and a s***ty husband […] but he had not been a rapist" (19.10). How's that for a Father's Day card? It's something, we suppose.