Switching Mohel’s for the Brisim of different children:
Some Poskim rule that once one has become accustomed to hiring a certain Mohel to perform the circumcisions of his sons then it is forbidden to switch and use a different Mohel for the circumcision of any future sons [without the original Mohel’s consent]. This certainly applies if one used the same Mohel for the circumcision of three sons, and some are stringent even after two sons, or even one son, to not use another Mohel. Nonetheless, despite the above opinion, many people are not particular in this matter, and rely on the dissenting opinions on this issue, as well as the established community custom, to not acquire the rights of circumcising one’s sons to any individual Mohel. However, in those communities in which it is customary to retain the same Mohel for all future sons after two sons have been circumcised by him, then one is to be stringent unless there is extraordinary reasons for taking a different Mohel [i.e. not available, found Mohel of greater righteousness or expertise].
 See Pesakim Veteshuvos 264:7; Otzer Habris p. 165; Kuntrus Idna Dechedvasa p. 61 article of Rav Shlezinger
 Rav Akiva Eiger 264:4 in understanding of Maharik Shoresh 76, recorded in Beis Yosef 264, “Just as we rule regarding Makirei Kehuna that it is forbidden for one to retract from the present up Teruma and Maaser to give, so to when is forbidden to retract from a Mohel who was accustomed to circumcise one’s sons.”; Nivchar Bakesef O.C. 4 “It is obvious that one who has received a Chazakah in doing a mitzvah then it cannot be removed from him as rules the Rambam and Maharik ibid”; Migdal Oz 53:20; Rashal in Yam Shel Shlomo Bava Kama 8:60; Mayim Amukim 70; Zechor Leavraham Chazaka; Admas Kodesh 2:130
 See Zechor Leavraham Chazaka; Admas Kodesh 2:130; Pesakim Uteshuvos ibid footnote 48
 This ruling of Maharik ibid is omitted in Michaber and Rama 264:1 and negated in Beis Yosef 264 who rules like Rosh 12:2 over the Maharik ibid; See Chacham Tzevi 70; Article of Rav Shlezinger ibid who completely negates the stringent approach and says it’s a misunderstanding in the Maharik, as even the Maharik only discussed a case that the Mohel received knowledge of the newborn child, and even he only discussed it from the aspect of Makirei Kehuna and not from the aspect of Chazakah; See there for other reasons of why the stringency doesn’t apply; Rav Eli Landa Shlita suggests that seemingly even according to the stringent approach, it only applies when the Mohel does the mitzvah for free, however when he does it in exchange of payment, then he does not acquire any rights to the Mitzvah. See the following Poskim regarding a similar ruling that a Chazan or Baal Tokeia is not a Chiyuv for an Aliyah on Rosh Hashanah or Yom Kippur if he is paid for his service: Elya Raba 584:9; Machatzis Hashekel; P”M 584 A”A 6; M”E 584:22; M”B 584:9; Kaf Hachaim 584:24; Vetzaruch Iyun!
 Zocher Habris 2:32; Pesakim Uteshuvos ibid that so is the widespread custom today do not be particular in this matter
 See Taz 264:5; Chacham Tzevi ibid