You can find the Ts and Cs for the Next Big Thing promo here:

http://goldpassport.hyatt.com/gp/en/....jsp?wt=pop_up

Free Night Award(s) can only be redeemed for stays between October 15, 2009 and March 31, 2010 and are not transferable. Free Night Award(s) are valid with standard room accommodations only and do not include incidental expenses, gratuities, service charges or other hotel-specific charges. Free Night Award(s) are valid for single or double occupancy. Additional guests are subject to additional hotel charges.

The rules are explicit that the room booked must be a standard room. If you are a diamond, the room that you personally occupy should be upgraded to a Regency Club on the day of arrival.

The rules do not explicitly state how many rooms can be booked at a property on a specific night. I would expect any family member to be able to book multiple rooms for children/parents. I find it a little worrying that the agent was taking a very strict line in saying you can only book one room for a NBT redemption. I've always understood with Faster Free Night redemptions that I could book a room for a friend, as long as I was physically present, occupying another room, and able to check them in.