I've just got back from DLRP and was actually surprised by them a little bit. After reading reviews of the Natama meals, and also some of the horror stories, I was really worried I would be living off snacks all week! I'm Coeliac and have a nut allergy so I ended up really confusing the cast members, but I did get some advice whilst I was out there that might help you out.
First off, go to disneylandparis.co.uk/content/GB/EN/Neutral/system/images/food_allergies.pdf. It is the DLRP Food Allergy information. It gives you all the information on the Natama meals as well as what you can get at breakfast. It also gives you a break down of the ingredients in each item, and they are telling the truth about not hiding any off the list. I would also make a point of either learning the French to explain the allergy, or have a look around the internet for an allergy travel card. brokerfish.com/food-allergy-translation-cards/nuts-french is an example of one for nut allergies. As a helper, Sans Noix (pronounced son no-ah) is nut free. Tell the hotel staff about the allergy and also when you make reservations for meals, as they will make a note about it on the reservation.
They are very new to the fact that people with allergies just want to eat normally, and not have an airline style meal, so do talk to them. I went to the buffet in the hotel a couple of times and just spoke to one of the chefs to find out what was in the food, plus the only real issue I had was the desserts, but there are ways you can avoid the things you can't have. As for not liking the Natama meals, I have to say that the soup and all the main meals I had were pretty good considering they are microwaved, and they are literally free from everything. Due to their over cautious attitude as well, there is nearly zero risk of cross contamination, just be warned you'll be opening the packets yourself as they are that cautious they don't remove the packaging.
One final tip, When all else fails, there is a supermarket one stop down on the RER at Val d'Europe that is huge and the phrase parlez-vous anglais s'il vous plaît is a must have in your French vocab to help make things that little bit easier.
