Yes, the lyrics of this song reflect the love of a father for his daughter.
I am guessing that the father was away from his daughter for a long period of time. Perhaps he was at war, or in a prison. The phrase It wasn't on a sunday (monday and tuesday went by) It wasn't on a tuesday afternoon (all I could do was cry)" could mean that the father's days just seemed to be the same from day to day. The specific names of the days had no significance to him because he was so sad to be away from home...each day was agonizing for him. The fact that the names of the days of the week are not capitalized (sunday, monday, etc.) reinforces this idea.
Yes, the father cried because he could not be with his daughter.