tell dad to schedule an appointment with his doctor  have the doctor
determine what type of allergies he has if he hasn't done this before    He
will need to get on allergy medication either prescribed or over the counter
if he is not willing to do this I  can't tell you what to do but her is  a
little information to ponder on
http://allergies.about.com/od/cats/

i think the belief is that allergies are caused by the cat's saliva.
there are products that can clean this off their fur and keep allergies
down, i've seen them in newspaper reports.
i googled and found this:
http://www.amazon.com/gp/product/B0002X30WU/103-2933347-3565424?v=glance&n=28450
7&v=glance
but you get the idea

the mayo's thoughts on the matter:
http://www.mayoclinic.com/health/pet-allergies/HQ01204

The ultimate way to see if the dad is allergic to the cat is to cook the cat
skinless and see if the allergies persist. If not you'll be able to cook
cat for him whenever one wanders by.