With the exception of embarkation day, one sit down restaurant is open for breakfast and lunch each day. The Dream and Fantasy have a separate "allergy kitchen" for special preparation.
OK, first add the allergy notation to your reservation. THen when you go to lunch on the first day, identify yourself to the head server--he or the chef will talk to you and bring you food from "untouched" containers in the galley or fix something for your family. Your assigned team will again review the issues with you at dinner that night.
OK, from that time on, when you go to the dining room everyone is asked for your room number. When you give the number, an "allergy alert" will appear on their screen, prompting then to again have you taken care of by the chef or head server. In many cases, you are provided with tomorrow night's menu so you can select something to be prepared in advance or altered to meet the needs of your family. And don't hesitate to ask about going "off menu". They'll meet your desires if at all possible.