Megillah 3b: The Megillah is read before doing the service in the Beis Hamikdash [or any other Torah mitzvah] .
Rema (OC 687:2): That is provided that both can be done, but if there is only time for one mitzvah, Torah mitzvos take precedence over Megillah.
Rema (OC 693:4): If there is a bris milah in shul, the custom is to do it before Megillah.
מגילה ג ע”ב: עבודה ומקרא מגילה ־ מקרא מגילה עדיף.
או”ח תרפ”ז ס”ב רמ”א: הגה וכל זה לא מיירי אלא בדאיכא שהות לעשות שתיהן אבל אם אי אפשר לעשות שתיהן אין שום מצוה דאורייתא נדחית מפני מקרא מגילה (ר״ן וב״י בשם תוספות ומהר״א מזרחי).
מ”ב שם סק”ט: ה״ה לענין מילה ומגילה, איכא שהות לעשות שתיהן מגילה קודם משום פרסומי ניסא [פר״ח ופרמ״ג] והעולם נוהגין למול קודם המגילה וכדלקמן בסוף סימן תרצ״ג. ח”א.
רמ”א תרצ”ג ס”ד: כשיש מילה בפורים מלין התינוק קודם קריאת המגילה. (מהרי״ל ומנהגים):
Alter Reuven Weingarten and his younger brother have the same birthday, 7 Adar, one year apart. He likes to tell the story behind it. Before his birth, his mother had gone many years without having a child. In those days, mothers used to be kept in the hospital with their babies for a week. It was difficult to get out in time for the bris. His father came to the hospital early on Purim morning to get her discharged, but the hospital would not let the mother and the baby go until he paid his balance of $7. Not having any money on him, he took a taxi to Williamsburg to get some money from home, and returned straight to the hospital. By the time mother and baby were discharged, it was Purim afternoon, and they came to the Satmar Beis Medrash for the bris. The Satmar Rebbe was waiting for them, in keeping with the minhag that a bris precedes the reading of the Megillah. The Rebbe had been pacing back and forth, and he was very upset that the bris was so late. The whole kehillah had been waiting a long time to hear the Megillah. They had the bris, and the Rebbe lained the Megillah very late in the day.
Afterwards the Rebbe held his Purim tish. Alter Reuven’s father was at first afraid to go – he didn’t want the Rebbe to yell at him. But then he decided he would go, come what may. He picked a seat in a far corner of the room. Suddenly they told him, “The Rebbe wants you.” He came over to the head of the table, and the Rebbe said, “Next year don’t keep us waiting so long!”
Read and Remember 