If a baby is sleeping or very quiet, there is no halachic constraint on holding or “wearing” a baby while davening, in public or in private settings. When a baby is awake and at any moment may make distracting noises or movements, common sense and, in public settings, sensitivity to others, should prevail. Shema and Shemoneh Esrei demand extra concentration, so they should be treated with greater caution.

Concern about a diaper should not preclude davening in a baby’s vicinity. As long as a baby is exclusively breastfed, even a bowel movement has no halachic bearing on prayer. Once a baby eats solids (or takes formula), and has bowel movements with an unpleasant odor, the diaper should be checked prior to prayer and changed immediately if any smell escapes from the diaper.

Please write back with any further questions.