Fries can be a tough one sometimes. You have to make sure that they are fried in oil that is not used for other breaded items. Alot of counter service type places cannot gaurentee no cross contamination. We had better luck with sit down restaurants. Here is some information on food allergies from the DL website;
Table-Service Locations
Table-service restaurants that accept reservations at
Disneyland Resort can accommodate most food allergies or intolerances.
Common Food Allergies include:
gluten or wheat
shellfish
soy
lactose or dairy
peanuts and tree nuts
fish
eggs
corn
Guests should notate these food allergies and intolerances at the time of booking their dining reservation. Guests are also welcome to speak to a chef or a manager on duty when arriving at the dining location.
Most restaurants offer no sugar added, low fat, low sodium or vegetarian options. Advance arrangements are not necessary for guests with lifestyle dietary requests. Guests can discuss this with their server upon arrival at the restaurant.
Metabolic Disorders/Multiple Allergies
Guests with requests associated with the list below should contact the Disneyland Resort via email at least 14 days prior to arrival and after booking all dining arrangements for the entire visit:
Allergy or intolerance not listed above under Common Food Allergies
PKU
Metabolic disorders
A single guest with multiple allergies/intolerances or multiple guests with allergies/intolerances within the same party
The restaurants will do their best to accommodate guest dietary requirements, but cannot guarantee they will be able to meet all requests.
http://disneyland.disney.go.com/plan/guest-services/special-dietary-requests/
I would suggest making reservations to make sure you can get the comfort food your DS need
