When I was a kid, men went to shul and women stayed home with the babies. This is logical as men are obligated to go to shul and women are not. In addition, women can nurse and are better with babies than men [with all due respect to us..] so it makes sense that they should be the care-givers, at least during davening.
Times have changed. I now see all over that men are taking even little babies to shul. Why? Don't these babies have mothers? Of course they do. How would they have been born otherwise?
If the mothers are not home then the men should stay home. Shul is not a place for babies. The fathers who are bringing their babies are not davening properly because they are constantly busy tending to the baby's needs and in addition the babies cry and disrupt the tefilla.
Today I saw a new one. Two kollel men took their babies to the beis medrash and learned afternoon seder with their chavrusos [when they weren't busy with the babies]. A busy beis medrash and crying babies?!
Really, really - they should stay home. If mommy can't be there and they can't find a baby sitter then using the beis medrash as a nursery is not appropriate.
We love babies. One day they to will be יושבי בית מדרש - just not yet at the age of three months.
Give them time....