If the Mom or Dad really, really, want a Shul bris, then I would have the bris after davening with a minimal kiddush. And have the Sedudat Mitzvah at home with family.
BUT, if the new Mom does not want to bring a newborn out in inclement weather, or walk to Shul in bad weather, I would honor HER wishes and have the Bris at home after davening followed by a family/close friends kiddush.
(FYI, my brother had his Bris on Simchas Torah, and that year it was pouring. The Bris & kiddush was held in the house. My Mom would not walk 10 blocks to and from Shul in the pouring rain with a newborn.)
Much, much Mazal Tov to you and your entire family.