The Latecomer Loses Out
Question: I recently attended a brit mila at which everybody stood around for a long time waiting for the mohel to arrive. In desperation the father of the child to be circumcised asked another mohel who lived nearby to do the mila. Just as he was about to begin, the first mohel showed up. What is the right thing to do in such a case?
Answer: There are several variations of this situation which are discussed by the halachic authorities:
1) The father ordered another mohel because he assumed that the one he originally ordered was out of town and would not arrive on time. The original mohel was in fact in town and arrived on time.
In such a case the first one should do the mila because the father never retracted his original order. (Rama in Shulchan Aruch Yoreh Deah 264:1)
2) The father ordered another mohel because the first one failed to arrive on time.
He did arrive after the mila was done and complained to the father and mohel about his mitzvah being taken from him.
In this case he is the victim of his own tardiness and has no claim on the father and the other mohel. (Zocher Habrit)
3) The case you mentioned in which the late-coming mohel does arrive before the other mohel begins:
If the second mohel already has begun to prepare the baby for the brit he should be allowed to complete the mila. If not, it would be preferable to allow the first to do the mila to save him from great embarrassment and to compensate the second one with some payment or by giving him some honor such as saying the blessings following the brit. (Rabbi Yitzchak Zilberstein, in his Aleinu Leshabeiach who adds that there is no need to wait more than half an hour for the first mohel.)