Very sorry to hear about your grandmother.
I agree aco22 100%. If this is new for the cat, than it probably is environment. Cats know when their owners are sick, plus with the new home, the cat is very stressed and is frightened.
Giving this cat a home where it is an only pet and no younger children may work out for the cat. If you dad is not a cat person, he may exaggerate the truth just a bit
. Cats with this personality type must approach humans on THEIR terms, not vice versa. Sounds like your parents home has too much activity in it for this cat.
Cat bites can be very infectious and your grandmother should not be exposed to such risks. Is there anyway you can take in the cat now?
Please keep us posted!