Is the husband obligated to begin with spending the night with the wife whose turn it was before his travel, and does her right to spend the night fall if she is with him in the same house but they do not share the same room?

You should start with the overnight stay and the division (of time) for the wife whose turn it was before your departure, because it is her right that became due before the journey, and it is obligatory to make it up. If you are all in one house as mentioned, then division (of time) becomes impossible, so it is postponed until you find a dwelling.