I agree....introduce them slowly. Keep the new kitty in your daughter's room for about a week. During this week rub your daughter's cat with a towel, then rub your cat with the same towel so they can start exchanging scents. Do this multiple times daily.
After a week lock up your cat and let your daughter's cat out for a couple of hours twice a day. Do this for a week.
After a total of two weeks have gone by, let them both out at the same time. As soon as they are out, give them each a yummy treat (like tuna) on opposite ends of the room. Do this several times daily (so give small treats), each time moving the bowls a little closer to each other. You want them to associate good things (treats) with the presence of the other cat.
If they are getting along right away you can leave out the new cat. But, if they still seem unsure of each other, I would have your daughter's cat sleep in her room at night. Once they can be together without being upset, you can leave them both out 24 hours a day.
Do not let them fight! A little hissing and growling and even a swat or two is expected. But, if one attacks the other, put the aggressor in time out (the bathroom) right away. Do not try to break up a fight with your hands. Instead use a squirt of water or toss (gently) a pillow at them.