Opening your mog house is an option available to you once you satisfy 2 conditions. First, you mist be in a group of 2 or more. Secondly you need to be in your mog house and not in a rent-a-room (moghouse in another city other than your home city.) Once these conditions are met, the Open moghouse option become available from the moogle when you talk to it. opening the house will allow anyone in your party ( not sure about alliances ) to enter your moghouse by talking to the NPC outside the residential area entrance.