When Purim and Megilah reading is Motza’ei Shabbos (Saturday Night) what is said first, Havdalah or Megilah–I will need to perform Melacha–driving to shul for Megilah
In shul the megilah is said first and havdalah afterwards. You have no problem doing melacha before the megilah by driving to shul, just make sure that you say “boruch hamavdil… first. It would be the same if someone would want to color their (or a child’s) face before going to the megilah, or carrying the megilah to shul motzei shabbos.
O:CH 693-1. Note: If someone if reading the megilah at home, there are opinions that one should act similarly to motzei shabbos chanukah, that some people light the candles first and others say havdalah first. Daas Torah O:Ch 693.
This does not apply to when the megillah is read in shul as in shul even on chanukah the menorah is lit before havdalah.