Enemies of parent-Parent instructs child not to befriend a person:[1]

If one’s father instructed his son not to talk with a certain individual, and to not forgive him, until the arrival of a certain date, then if the son desires to make peace with the individual right away, he may do so and ignore his father’s request.[2] [Thus, it goes without saying that a son may not continue or assist in a heated dispute that his father has with an individual even if his father instructs him to do so, and even if it appears to him that his father is in the right. On the contrary, he should try to make peace between the parties, as aside for the great mitzvah of making peace, perhaps his father is truthfully in the wrong and is simply blindsided.[3] Nonetheless, the son should not openly befriend the enemy of his father if this will cause the father to become upset.[4] Some Poskim[5]  write that the above prohibition only applies in the case that the reason for the fathers instructions is due to hate, and indeed the son will come to hate the individual. If, however, the father’s instructions will not lead to the son hating the individual and was not given an order so he hate the individual, then it is permitted for the son to follow the instructions. Thus, if a father instructs his son not to talk to an individual due to the bad influence that he will have on him, then his son is to obey his instructions.]

Father instructs his son not to say Kaddish for his mother:[6] The father may not protest his son from saying Kaddish on behalf of his mother.[7]

Father instructs son not to learn Torah from a certain Rabbi:[8] If a person would like to learn Torah from a certain Rabbi and his father tells him not to learn Torah from him due to a certain dispute that he has with that Rabbi, then one should not listen to his father as it is as if his father is telling him to stop learning Torah.

Not to befriend a person who belittled and shamed his parent:[9] One is to distance himself from people who speak against his parents or belittle them, and he should therefore avoid speaking with them. [Accordingly, although it is forbidden for one to hate an individual who is in a fight with his father even if his father instructs him too, nonetheless, this only applies if the father himself is not allowed to hate  the individual. However, if the father himself is permitted to hate the individual due to his actions, such as if the individual belittled or shamed the father[10], then it is  likewise permitted for the son to hate him. This especially applies if the person caused one’s parent so much pain that it caused the parent to get sick and shorten his life. In such a case it is a mitzvah for the son to hate such an individual due to the command of respecting one’s parent.[11]]

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[1] Michaber 240:16; Tur 240; Shut Rosh 15:5; Pesakim Ueteshuvos 240:47; Encyclopedia Talmudit ibid p. 439 footnotes893-897

[2] The reason: As it is forbidden to hate any Jew unless one witnessed him transgressing a prohibition, and hence this instruction of his father is similar to an instruction to transgress words of Torah. [Shach 240:18; Taz 240:16; Beir Hagoleh ibid; Shut Rosh ibid] Now, although there is no actual prohibition against hating a Jew if one simply stops speaking with them due to his father’s instruction and not do to an intrinsic hate, nonetheless, since the father’s intent is so the son hate him, therefore it is forbidden to be done. Alternatively, since the father himself transgresses the prohibition against hating a Jew by instructing his son as such, therefore the son is no longer obligated to listen to him. [Kneses Yechezkal 35; Shem Aryeh O.C. 1] See Pesakim Ueteshuvos 240:47 footnote 407

[3] Shemiras Halashon Shaar Hazechira 17

[4] Chesed Lealafim 240:12

[5] Sefas Emes 240; Pesakim Ueteshuvos 240:47

[6] Rama 376:4; Rashal in Yam Shel Shlomo Kiddushin 63; Pischeiy Teshuvah 240:14

Other opinions: Some Poskim rule the son is not allowed to say Kaddish for his mother if his father protests. [Rivash 115, brought in M”A 132:2; Option brought in Birkeiy Yosef 240:8-10 being that saying Kaddish is not a Rabbinical Mitzvah but a custom; Poskim brought in Pnei Baruch 34 footnote 38; See Pischeiy Teshuvah 240:10-11 in name of Teshuvos Rav Akiva Eiger 68] Some Poskim suggest that possibly the son may choose to do whatever he wishes, and if he wishes to respect his father, he may stop saying Kaddish. [Option in Birkeiy Yosef 240:8-10]

[7] The reason: As the father transgresses the Mitzvah of Veahavta Lereiacha Kamocha. [Rashal ibid, brought in Pischeiy Teshuvah 240:14; 376:5]

[8] Maharam Mintz 15

[9] Birkeiy Yosef 334:7 in name of Mishpat Tzedek 3; Pesakim Uteshuvos 240:24 footnote 204

[10] See Admur C.M. Hilchos Ovrei Derachim Halacha 10 “Or his friend sinned against him and caused him a pain of the body in which case he is not required to remove the hatred from his heart and forgive him until he asks for forgiveness”; Admur O.C. 156:3 [implies allowance is only for Torah scholar]; 608:4; M”A O.C. 156:2; Yuma 23a; P”M O.C. 156 A”A 2; Imrei Yaakov Biurim on Admur C.M. ibid in great length

Monetary damage: If an individual caused one’s father monetary damage and loss and did not shame or belittle him, then if this was done for no reason then some Poskim rule that one may hate the person who did so. [P”M O.C. 156 A”A 2] However, from other Poskim it is evident that one may not hate a person who caused him monetary pain and it is only permitted if he shamed him and caused him pain of the body. [See Admur C.M. Hilchos Ovrei Derachim Halacha 10; Imrei Yaakov Biurim on Admur C.M. ibid in great length] See Shut Maharshag 2:53

[11] Minchas Elazar 4:13; Pesakim Ueteshuvos 240:47; See Pischeiy Teshuvah C.M. 426 in name of Tzemach Tzedek 111 regarding the mitzvah of Goel Hadam