New Cat Big Noise

So we adopted another cat "Stretch" and have been slowly introducing him to the household. Well the girls Stella our youngest and Sadie our first adoptee who is 8 are not happy. Sadie handles things a bit better, she whacks and hisses but Stella is beside herself and is reacting as if Stretch is killing her even when he is just approaching her. Now Stretch has been very good making approaches and then patiently backing off but it is wearing thin and Stella is just not adapting yet and is still acting as if he is the worst thing that has ever entered the house. So today he lost patience and whacked her and chased her around and poor Stella pooped on the floor and I had to put her in the bathroom to calm down. He isn't being mean or even trying to hurt her, I watched and his ears were not back and he didn't seem to have claws out, but I think he has had enough. And all this drama is not going over well with the alpha lady of the house who finds it very unerving. So I don't know what to do but I am going to ask our cat specialist lady what to try next.