Is the Mitzvah to honor one’s parents considered a Mitzvah between man and G-d [i.e. Bein Adam Lamakom] or between man and his fellow [i.e. Bein Adam Lechaveiro]?
Some Poskim learn that the mitzvot honor one’s parents is a Mitzvah between man and G-d and not between man and his fellow. Other Poskim, however, learn that it is considered a Mitzvah between man and his fellow, and not between man and G-d. Other Poskim leave this matter in question. The Rebbe and others learn that it contains both aspects. There are a number of practical ramifications between these two approaches, including if one must ask forgiveness from his parent if he did not properly fulfill the Mitzvah, as will be explained next.
Must one ask forgiveness from his parents if he does not fulfill this Mitzvah properly?
This matter is dependent on the above debate. According to the first approach [Bein Adam Lamakom], one is not required to ask forgiveness from his parent. According to the second approach [i.e. Bein Adam Lechaveiro], he is required to ask forgiveness from his parent. [Practically, based on the Rebbe’s conclusion, one is to ask Mechila from his parents if he did not properly respect them.]
Must one have intent to fulfill the Mitzvah of honoring and fearing one’s parents when doing an act of honor or fear in order to fulfill the Mitzvah?
No. Since the Mitzvah of honoring one’s parents is a Mitzvah that is between man and his fellow, and the main aspect of it is what the parent receives, therefore, intent is not required in order to fulfill it. Furthermore, even if one explicitly has counter intent to not fulfill the Mitzvah by doing a certain act of service for one’s parents, the Mitzvah is still considered fulfilled.
 See Minchas Chinuch Mitzvah 33; Pesakim Uteshuvos 240 footnote 23; Likkutei Sichos 19:197; Likkutei Sichos 36:90 and 95 and footnote 8; Encyclopedia Talmudit Erech Kibbud Av Vaeim Vol. 26 p. 374
 Ramban Al Hatorah Shemos 20:12-13 that the first five Dibros are Bein Adam Lamakom [However, see Ramban 20:12 from which one can understand that he holds its Bein Adam Lechaveiro, as writes Abarbanel ibid in his opinion. See Likkutei Sichos 36:90 footnote 4]; Implication of Even Ezra Yisro 20:1; Implication of Chizkuni 20:13; Tur Al Hatorah ibid; Ikarim Mamar 3:26; Abarbanel Shemos ibid [writes like Ramban ibid, however then also writes its Ben Adam Lechaveiro]; Shelah Miseches Shavuos 190; Chemdas Yisrael Ner Mitzvah 10; Likkutei Sichos 36:90 and 95 and footnote 8 that it contains both aspects of Bein Adam Lechaveiro and Bein Adam Lamakom; See Keli Yakar and Chizkuni on Yisro ibid
 Rambam Pirush Hamishnayos Peiah 1:1; Rosh on Mishneh ibid; Kuzari Mamar 3:11; Abarbanel Shemos ibid; Likkutei Sichos 19:197, printed in Shuchan Menachem 4:173 that it is a Mitzvah Bein Adam Lechaveiro; Likkutei Sichos 36:90 and 95 and footnote 8 that it contains both aspects of Bein Adam Lechaveiro and Bein Adam Lamakom; See Keli Yakar On Yisro ibid; See Kiddushin 31a which implies that it is a mitzvah between man and his fellow “Ula taught: After hearing the first two of the 10 Commandments which instructs one to believe in G-d and that serve other deities, the nations of the world said that the 10 Commandments were given by G-d for the sake of His own personal glory. However, after they heard the command to honor one’s parents they retracted and acknowledged the first commands.”; See Yireim Hashaleim p. 5; Rashba 1:18
 Minchas Chinuch ibid
 Likkutei Sichos 9:XV; 36:90 and 95 and footnote 8; Beir Yehuda on Chareidim p. 72; See Likkutei Sichos 36:96 that there are two aspects in the mitzvah of honoring one’s parents, one an intellectual moral aspect which is between man and his fellow, and a second which is between man and God, as through honoring one’s parents one honors God. The Rebbe there explains that only the former aspect is relevant to Gentiles, while the latter aspect is only relevant for Jews, as only by Jews is the infant light of God united with their bodies, and hence does honoring them not consist of idolatry, in contrast to Gentiles in which honoring them with consist of Shituf.
 Minchas Chinuch Mitzvah 33; See Ben Ish Chaiy Vayelech 1:6; Encyclopedia Talmudit ibid; Likkutei Sichos 36:91 footnote 8
 Oneg Yom Tov O.C. 19; Sdei Chemed Mareches Mem Kelal 68; Likkutei Sichos 19:197, printed in Shuchan Menachem 4:173, based on Kiddushin 39b which brings the opinion of Rav Yaakov that there is no reward of a mitzvah in this world from the fact that a boy died in the process of climbing down the tree after getting the baby birds on behalf of his father. Now, if intent were to be required to fulfill this mitzvah then there would be no proof from this story as perhaps the son did not have intent to fulfill the mitzvah upon doing so, and hence he was not deserving of the reward of life. The fact that this option is not entertained by the Talmud shows that intent makes no difference in this matter and either way the mitzvah is considered fulfilled; See Sifri Ki Seitei 24:19 for a similar ruling regarding tzedakah the main thing is that the pauper received the charity irrelevant of what intent the giver had; See Malei Haroim Erech Mitzvos Tzerichos Kavana 9 regarding the mitzvah of circumcision that the mitzvah is fulfilled by physically doing the circumcision even if there wasn’t intent to fulfill the mitzvah; Likewise, see Minchas Chinuch Mitzvah 1 regarding the mitzvah of having children, that the mitzvah is fulfilled once one has a male and female child even if there was no intent to do so for the sake of the mitzvah