If I remember right, the printed guide issued to 1st Class passengers specifically mentions only the dining room at regular meal times as a no-go area for children. In most respects there were no hard and fast rules laid down because it could be expected that passengers would behave according to the conventions of their particular level of society. Where that didn't work, a polite suggestion from a steward would generally suffice.
Thus it wasn't really necessary to place a 'men only' sign on the door of the Smoking Room, or to formally ban children from areas where they might disturb the peace of adults. At the higher levels of society at home, most families preferred their children not only to be 'seen and not heard' but preferably not seen much either! They lived in their own part of the house under the care of servants, and were expected to be on their best behaviour when in the company of Mama, Papa or their friends.
In 3rd Class, of course, home life was very different and the whole family lived together. On ship, nobody would expect any change in those arrangements so children were to be found in all public areas and enjoyed a lot more leeway in terms of acceptable behaviour, though respect for their elders and immediate obedience was still expected. If the young 'uns became too boisterous, a sharp "Oi! Behave!" would generally restore order; if not, retribution would be swift and effective (and not much resented).
.