What your mother seems to be having is cooking oil food allergy. Vegetable oil is usually a blend of oils. The refining process removes proteins from the oil. Since it's the proteins in oils that can cause allergic reactions, sensitive people probably won't react to refined oils. Some speciality oils, such as sesame and walnut, aren't refined and can cause allergies.
I suggest you to consult an allergist for your mother and get food challenge test done to confirm the diagnosis.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.