In Agricola, do family members occupy as many rooms as possible?
The third member will occupy the third room of your house, even if you use the "Family Growth even without a room" action.

The relevant rule starts on page 9 of the rule book, under "Family Growth even without a room":


  Note: If a player who uses this card later extends her home, she may not use the other Family Growth card again until she has more rooms than Family members: the new rooms must first be used for Family members that did not previously have their own rooms.


This means you cannot take the actions in the order you are suggesting without building an additional room between the two "Family Growth" actions.