Do not, do not encourage your niece to extend a hand down to an upset, fighting cat. She should grab a pillow and put that between the animals.
I have a friend who thrust an arm between two fighting cats (her own pets) and one of them attacked her arm. The result was a serious injury (he had torn a nerve) and a bad infection.
There ae books, etc, which will tell you the same thing. Not a hand, a pillow.