Got a similar family situation, forces wife and child travelling to and from the Mediterranean from England.
I know, from family knowledge, the dates of travel and the ship's name, it was the same ship on both voyages, and I've got the mother's passport and also her travel docs from the ship.
That ship was a troopship, although in peacetime it also carried a lot of unaccompanied forces dependents, and also civilian passengers.
At the time in question, early 1950's, it was on a regular route to and from the Far East via the Mediterranean.
Checked every passenger on the passenger manifest for the relevant voyages, also checked for name spelling variations, nothing, they aren't listed.
So, I can only conclude that forces dependents were listed separately on a forces manifest which hasn't been made publicly available, at least not on the internet.