me thinks you need to be 18 or over to apply for naturalisation.
but for under 18's its possible to Register as British, when your wife applies for Naturalisation the child details should be entered on to the form in the appropriate place. So when the parent gets Naturalisation the child will get Registered as British.
The difference between Naturalisation and Registration? Once granted, effectively none at all. However at the application stage there are differences. For example no Citizenship Test needs to be taken by anyone to be Registered as British.
cost of naturalisation for the wife is i think £655
registration for your stepdaughter i think is £400.
but you better check what i've said is correct with ukba