I think this song is about the man who Mark's mother is with, though I'm not sure about it being his father.
He mentions the year 1983, well Mark was born in 1972, so it would have made him 11 years old. I think the man who Mark's mother was with, was abusive towards her. He tells his mom to drive them away, but she say's there's no where to stay. Many women suffering abuse from their partners are often too frightened to just leave them.