There was no particular stricture concerning children. Parents were responsible for their decorum and cleanliness; that's all. They could enter as far as the parents were allowed to enter. During the yearly festivals, young children (not babies) were expected to come with the parents (Talmud, Hagigah 2a).Everyone who entered the premises had to ritually immerse beforehand (Talmud, Yoma 30) to ensure ritual purity.