We are onsite people so I will address it in that way. Legally with four people you can stay in any room.I think you will just need to balance your budget with your comfort requirements. If you need to be super budget, you can get one room at the values, a bed for mom, one for you and your DD and bring an air mattress for your DS. Going to be a little cramped and a little bit of a pain to deal with moving the air mattress but certainly doable. Two value rooms might be a great choice IF it works for your budget. If you want a little bit more room in one room, choose a moderate or a deluxe, one room and bring that air mattress or if choosing a deluxe, you will have an extra sleep space in SOME rooms. If money is less of an issue than comfort, a cabin at FW would work well, or look into renting DVC points and staying in a DVC resort though this would be more costly.
Off site, the same. Air mattress in a standard room or look into a two bedroom condo or home.