Just choose one and use it consistently. Alternating will probably stick out like a sore thumb and annoy readers. I would probably go with dad, or maybe father if the narrator has a more formal voice*. Sid seems weird to me. I always call my parents mom and dad, and can't remember the last time I actually referred to them by their names. Maybe other people are different, so take that with a grain of salt. However, since you mentioned that the narrator and his father are estranged, using Sid could suggest that the narrator doesn't consider him to be his father after being gone for such a long time.
*I'm assuming you're writing in first person, since the narrator is also a character in the story and you used the phrase "my father" rather than just father. If you're writing in third person, I would probably reverse this advice and prefer father over dad.