Is this referring to you, or to your brother? That wording is highly confusing in English. If it were you, it would be "my dad got a call at work because his son was...", and if it was your brother it would be "my dad got a call at work because his other son was..." . You would never say "my dad's son" to refer to yourself.
It's referring to myself, and I know you'd never use that wording normally, I did it for comedic effect (specifically, to keep the phrasing in line with the preceding parts). But you know what they say about German humor …
Is this referring to you, or to your brother? That wording is highly confusing in English. If it were you, it would be "my dad got a call at work because his son was...", and if it was your brother it would be "my dad got a call at work because his other son was..." . You would never say "my dad's son" to refer to yourself.