Your TA will have your room assignement about two or three weeks before your sailing date in most cases. SOmetimes you must wait until you get to the pier before you find out your cabin.
Your room will consist of two lowers and two uppers or one upper and a sofabed depending on the cat cabin you end up with. 95% chance it wilol be two lowers and two uppers.
You will need either a passport or your original issued birth certificate and a photo ID such as a drivers license for the adults. The kids will need their original issued ID's or passports, no photo necessary. Now if the kids have a differant last name make sure you have the dsocumentation to show why. If one or both of the children are step kids or adopted then you need either the signed permission of the absent parent to take them out of the country or documentation for the adopted child.