Translation:Dad is sitting near the door and smoking.
Passive voice is when the object that is being acted upon becomes the subject - "tobacco is being smoked". "Dad is smoking" is in fact not passive voice, it's present continuous tense.
You're right though that the sentence is ugly, but it's because of the mixing of tenses. "Dad sits near the door and smokes" has a different meaning from "Dad is sitting near the door and smoking". The two don't really combine.
Edit: the suggested translation has been changed - as it is now it's fine.
You're right about the infinitive (it was late at night or early in the morning), but "to be" plus verb is passive voice, so "is smoking" is still passive. And mixing active and passive is bad writing in English. Switching "voices" within a sentence is certainly bad form: "One further caution about the passive voice: we should not mix active and passive constructions in the same sentence."