well....as far as I can tell, it should definitely not be the problem finding a hotel, the problem most often is, finding the right one....as you can imagine with Hamburg being such a big city, there are soooo many hotels that you go crazy if you look at all of them...there is a page...
http://hamburg.topicbook.co.uk that has a nice overview of hotels and other interesting stuff in hamburg, that your family should definitely look at before they come. trust me its a huge amount of interesting information. ALL IN ENGLISH!!! the hotels are categorised by "stars" and each category is organised starting with the lowest price. and when holding the mouse on them, youll get a descritption. Pretty NEAT! So depending on what youre looking for exactly, I'm sure youll find something there.
about the hotels again....there is the "Hotel Graf Moltke" or "Hotel Commodore" but really I dont want to suggest anything, because I havent actually been staying in hotels in Hamburg, because I live in hamburg myself. So really I would suggest you check out the page (linked above), because I am 100% sure youll find what you need.
i hope itll help...good luck and enjoy your stay in my favourite city in Europe....