Is there any reason why the URLs should change each week? If I've understood you right, you will have a page showing hotels where rooms are available within one week from today, another page where rooms will be available within two weeks from today, and so on. Within each of those time frames, can you not simply use the same URL?
So, your URLs might be:
Each time a visitor requests a hotel room within a given number of weeks, your server-side code would query your database, generate an HTML page that contains the required data, and serve it from the URL in question. That way, the URLs will never change, and you will have no problem with search bots.
Also, don't get over-obsessed with sitemaps. A sitemap is only needed if you have pages which can't be reached through your normal navigation. Whether or not you have a sitemap won't make any difference to the particular issue you described.