Here's another tricky question about Halakhot of honoring parents (Shu"A ר"מ-רמ"א). I rewrite it to change the line of thinking.
THe Gemmorah (Kid 30b, also Mishna Kritus 6,9 "**האב קודם לאם בכל מקום") states that as long as they are married, honoring the father takes precedence over the mother (when in contradiction or at the same time). The reason is that she's subordinate to him by the marriage contract (as long as they are married).
When comparing honoring his father vs his Rabbi, the Rabbi takes precedence, because "the father brings him to this world, and the Rabbi to the world to come" (B"M 33a). The Gemmorah there proves that anyone who taught him a single Halacha deserves to be called Rabbi.
The father has numerous Torah obligations toward his son (Kid 29a), such as Milah, Pidyon, learning Torah, educating for Mitzvos (let alone his obligatory financial support). So there's no way he does not teach his sons some Torah or Halakhah. Therefore in my understanding, he automatically falls under a category of "a Rabbi" (of some kind).
However the Mom is totally exempt from all those - and does not usually teach the Torah or educate for Mitzvot. Therefore I conclude, that honoring the father (as a part-time Rabbi) must take a precedence over his mother when divorced.
However, the Gem. concludes differently: once they are divorced - they are equal in honor and the child can pick one randomly.
The question: given #3, why would honoring the father equal to that of the divorced mother?