There are a variety of allergy tests available and each has it's pros and cons.
Skin prick test uses a small drop of the allergen placed on the skin over a small scratch made with a sterile instrument like a needle - the doctor then analysis any reaction that is seen on the skin to make a diagnosis. As far as I know you don't need to have the allergen in your diet with this test.
Blood tests look for antibodies. For this you need to be eating or in contact with the allergen. I bought one of these tests last year at an allergy show and my results showed that I am not allergic to milk or wheat but was to animal fur and pollen - I don't eat wheat or milk as they make me ill. If you go down this route you will have to check with the doctor, clinic or lab as to how much to eat and for how long before hand. In the UK the guidelines for diagnosing Coeliacs disease is a minimum of 1 meal containing wheat/gluten everyday for at least 6 weeks.
Blind food trials are used for fast acting allergies by giving the individual the allergen to eat or drink and waiting for a reaction. for example a milk allergy might be given a few drops of milk then increasing the volume to a full glass to see if a reaction is had. What the medical staff and patient don't know is if the 'milk' is really milk or a substitute - hence it is a blind test. only the dietitian that prepared the drink knows what went in it. This needs to be done in a medical setting generally as a safety measure.
Passive Resistance testing is a homeopathic testing method that is not generally accepted by the medical profession. its basically has you hold a sample of an allergen in one hand while the tester pusses on the other arm. I had this done when I was 14 and came out with a very long list of allergies - most of my list I do react to in some way or another but others have never made me ill in any way. This method doesn't require a consumption of the allergen but as the same time it isn't a widely used and accepted testing method.
My advice would be to speak to your doctor about getting the girls tested. If he already knows that they have such a restricted diet then he can advise a suitable test. If he doesn't know then he will likely ask why you have restricted their diets and want so background and their symptoms. either way he can refer you to an immunologist for further tests. Just bare in mind that regardless if any test results, you can still have an adverse reaction to something as everyone is unique and so are their tolerances.