Reciting Shehechiyanu during Sefira-Part 1:
A. The letter of the law & custom:
The custom: Nevertheless, despite the letter of the law, many are accustomed to abstaining from saying the blessing of Shehechiyanu throughout the entire weekday period of Sefira, from after Pesach until Erev Shavuos. Practically, so is the Chabad custom, to avoid saying it. However, those who are accustomed to not abstain from saying Shehechiyanu throughout the period of Sefira may continue to do so without hesitation, as is the letter of the law.
B. Days when Shehechiyanu may be recited:
Shabbos: Even those who are accustomed to abstaining from reciting Shehechiyanu during Sefira may recite it on Shabbos during Sefira, and so is the Chabad custom. However, some Poskim write that one is to avoid reciting Shehechiyanu during Sefira even on Shabbos.
Chol Hamoed Pesach: Even those who are stringent not to recite Shehechiyanu during Sefira, may recite it during Chol Hamoed Pesach.
 See Sefer Chikrei Minhagim 3:79
 Mamar Mordechai 493:2; Levushei Mordechai 3:153; Ikarei Hadat 21:17; Yifei Lalev 3:3; Keren Ledavid 119; Orchos Yosher 11:133; M”B 493:2 in name of Mamar Mordechai; Kaf Hachaim 493:4 that so is the practical custom and ruling.
 The reason: This is no different than the allowance for an Avel to recite the blessing of Shehechiyanu during his period of Aveilus. [See M”A 551:42; Sefer Chassidim 840; Birkeiy Yosef 551:15; Kaf Hachaim 551:204; See however Binyoman Zeev ibid; Glosses of Chasam Sofer and Yad Efraim] Now, although we rule that during the period of Bein Hametzarim one is to be careful to avoid saying the blessing of Shehechiyanu [Michaber 551:17; Teshuvah Ashkenazim in name of Sefer Chassidim; Drashos Maharil Tisha B’av; Teshuvas Maharil 31; Agguda Brachos in name of Kolbo; Binyoman Zeev 163; Kneses Hagedola 551; Sefer Chassidim 840], and the reason for this is because since the period of the three weeks is a time of suffering, therefore one should not bless Shehechiyanu which contains the words “Lezman Hazeh” this time [a time of suffering]. [M”A 551:42; Sefer Chassidim 840; Birkeiy Yosef 551:15; Kaf Hachaim 551:204; See however Binyoman Zeev ibid; Glosses of Chasam Sofer and Yad Efraim] nevertheless, this only applies by Bein Hametzarim due to the destruction of the Temple which occurred during this time which is more severe than the mourning period of Sefira. [Mamar Mordechai 493:2; Kaf Hachaim 493:4]
 Custom mentioned in Elya Zuta 493:1 in name of Rabbeinu Yerucham 1:5; Leket Yosher p. 97; Makor Chaim of Chavos Yair; Likkutei Maharich; Tzeror Hamor Emor; Olalos Efraim 1:107; Mahariy Shteif 249; Moed Lekol Chaiy 6:12 [regarding new clothing]; Yifei Lalev 2:7
 The reason: The reason for this is because the period of the three weeks is a time of suffering, one should not bless Shehechiyanu which contains the words “Lezman Hazeh” this time [a time of suffering]. It is however not due to the mourning period, as we do not find that a mourner may not recite Shehechiyanu. [M”A 551:42]
 Hayom Yom p. 48; Sefer Haminhagim p. 84 [English]; Sefer Hasichos 1989 Vol. 2 p. 745
 Rebbe in Sefer Hasichos ibid; Kaf Hachaim ibid
 Leket Yosher ibid
 Sefer Hasichos 1989 Vol. 2 p. 745 in dialogue with Rav Mordechai Eliyahu and Rav Shapiro; Otzer Minhagei Chabad p. 258
The contrast to the law during Bein Hametzarim: In Sefer Haminhagim p. 94 it states not to recite Shehechiyanu on Shabbos of the three weeks but omits it with regards to Sefira. Hamelech Bemesibo quotes the Rebbe to have stated that he did not hear from the Rebbe Rayatz as what is the custom on Shabbos of Sefira and he hence did not enter it into Hayom Yom. However, in the above Sicha the Rebbe clearly states it may be said. [see Otzer Minhagei Chabad p. 258]
 Makor Chaim of Chavos Yair; Yifei Lalev 2:7 brought in Bitzel Hachachma 18:41; Vayivarech David 59
 Leket Yosher ibid
 Sefer Hasichos 1989 Vol. 2 p. 745 in dialogue with Rav Mordechai Eliyahu and Rav Shapiro
 Tzitz Eliezer 18:41 in name of Ben Ish Chaiy