This is something that I have heard and been taught many times, but I can't find it sourced anywhere. I do see this concept quoted often in various articles (via Google searches). The question on this division would be why is Kibud Av categorized as Ben Adam Lamakom.
The Ramban to Exodus 20:13-14 says this idea. I'm not sure if he is the first.
והנה עשרת הדברות חמשה בכבוד הבורא וחמשה לטובת האדם, כי כבד את אביך כבוד האל, כי לכבוד הבורא צוה לכבד האב המשתתף ביצירה, ונשארו חמשה לאדם בצרכו וטובתו.
And behold, the Ten Statements (Commandments) are five for the glory of the Creator and five for the benefit of man - as Honor your father and your mother is [for] the glory of God, as for the glory of the Creator did He command to honor the father that participated in the formation [of the child]. And five remain for man - for his needs and for his benefits.
You see he addresses your last point, that honoring one’s father and mother is considered honoring Hashem (see Kiddushin 30b).
See also Beis Elokim Sha’ar HaYesodos Chapter 12.