Marital relations:

It is forbidden to perform marital relations on the 1st night of Pesach.[1] This applies to the first night of Pesach; it is however permitted to be performed on the second night of Pesach.[2] Some Poskim[3] however rule that in the Diaspora it is not to be performed on the first two nights of Pesach.

Mikveh Night:[4] If the night of Pesach is the night of Mikvah then one is obligated to have intercourse that night. [One who refrains from doing so is considered as if he is performing a Mitzvah as a result of an Aveira.[5]]

Strong desire:[6] Those who feel a strong desire, or are troubled by forbidden thoughts, it is better for them to have intercourse than to come to doing a sin.

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[1] M”A 240:3; Siddur Yaavetz; M”B 240:7; Arizal in Shaar Hakavanos p. 86; Peri Eitz Chaim Shaar Chag Hamatzos 5 and 8; Oar Tzadikim 32:5; Moreh Batezbah 7:218; Kaf Hachaim 240:5; See Kaf Hachaim 481:16

The reason: As the sublime effect of Zivug is automatically performed by Hashem on the first night of Pesach without needing a physical Zivug occurring below, hence leaving no need for it to be performed on the first night of Pesach. [Peri Eitz Chaim ibid]

[2] Peri Eitz Chaim ibid; M”A ibid; M”B ibid

[3] Or Tzadikim 27:11; Kaf Hachaim ibid; Taharas Yisrael 240:11 in name of Poskim; See Piskeiy Teshuvos 240:10

[4] M”A 240:3; Admur 494:3 regarding Shavuos; Chesed Lialafim 240:3; Siddur Yaavetz; Chayeh Adam 130:22; M”B 240:7; Kaf Hachaim 240:5

[5] Shlah p. 213 brought in Kaf Hachaim 581:86 regarding the night of Rosh Hashanah

[6] M”B 240:7; 581:26; Kaf Hachaim 240:5; See Seder Hayom brought in Kaf Hachaim 581:86; Machazik Bracha 581:4; Ben Ish Chai Netzavim 9; Chayeh Adam 139:7; Kaf Hachaim 581:88.