It is pretty soon for her to just come out and blend with the family. She has to get used to the new vibrations she feels on the floor, the new smells, the new sounds, etc. Be patient with her, keep her in the room where she is at right now, secluded from the others. Take an old teeshirt of yours you don't care about and put it on and go mow the lawn, ride your bike, run around the block, walk to the store, just get it really sweaty. Put the shirt in the room with the cat and place tasty treats on the shirt, she will come out and eat (probably when you leave), and she will associate your scent with pleasant things. Go in and just sit on the floor and read out loud to her, or just talk to her in a soft voice (this gets her used to your voice) For the two cats to meet the best way I have found to introduce them is through a closed door. Take two favorite cat toys, and tie one toy to each end of a long string. Put one toy in the room where the cat is, and put the string down on the floor, run it through the open dooway and then shut the door. You now have one toy on one end and one on the other. When your resident cat sees the toy, she will attack it, it will move the other toy in the closed off room, and kitty should see this. Because kitty is alone and relatively safe, her prey instinct should be aroused and she will play on her end as well. Eventually, the two will meet under the crack in the door (as the toy gets pulled towards the barrier) and they will growl and get to know each other that way. Another thing to do is to take an old towel and start massaging each animal, do the new kitty first, then the resident kitty, then the dog, do this about 3 times, then do the new kitty with the same towel. Leave the towel in the room for the new kitty as well to help blend smells. (warning, she will probably pee on it, and that is a good sign) but if she doesn't then take it out after three days and rub your other animals down with it.
Just give her time, cats love familarity and her normal world was just shook upside down. I would also first and foremost take her to the vet to be sure the stress she is under hasn't made her ill.