My DS has several allergies (including animals) that trigger asthma and other allergy symptoms - he had no problems at AK. I guess it would depend on how severe your mother's allergies are. His allergies to animals are triggered by being in very close contact or by petting or touching an animal. The Safari and the Trails just didn't put him close enough to anything for it to be a problem. Plus, he takes medication daily to try and keep things under contol.
We are never caught without an inhaler and Benadryl...but he never used either in AK. However - allergies cannot be compared person to person - everyone's triggers, tolerances, and reactions are different. If your mother's allergies are severe, she probably just doesn't want to risk an episode that could affect the rest of the trip.
If other's hearts are set on AK, perhaps you could show her some pictures of AK online that would give her an idea of how close she would really be to the animals and show her a map online where she sees how spread out it is and then she would better be able to judge if it is going to be a problem. (And, you could decide to skip things like Rafiki's Planet Watch.) Maybe she's being conservative simply because she's unfamiliar with AK and wants to err on the side of caution. If you can show it to her "virtually" - then you'll both probably feel more comfortable with whatever decision is made.
Have a great trip!