No, it’s not acceptable.
In order to get the Mitzvah of hearing the Megillah, each man AND woman must hear every word. He or she certainly can’t do that if the babies and small children can’t sit quietly and not make noise, and if the babies and children have to be constantly shushed.
There is usually more than one Megillah reading at night and in the morning. Do the correct and decent thing, and leave your children with someone who has already heard the first Megillah reading, or who will hear the Megillah reading after you’ve attended the first Megillah reading.
The Shul today takes the place of the Bais HaMikdash (from “Praying with Fire”). Besides your being able to get the entire Mitzvah of hearing the Megilla reading, your leaving children at home (who can’t behave properly in Shul) teaches them that they can’t come to Hashem’s House until they can sit quietly and daven or listen to the Megillah, because Hashem’s Presence is in the Shul, and one must behave with Respect towards Hashem, the King of Kings.
A Shul is not a playground or a baby-sitting service.
If you took a child to work with you, one day; would you let the child run around and make noise?
So would you let your children run around and make noise in the Bais HaMikdash, the House of the King of Kings?
So why would you bring to Shul (which is in the place of the Bais HaMikdash today) or a Megillah reading, babies and small children who cannot sit quietly?