New cat attacking current cats

I recently brought in another cat in to my home. She was from a multi cat and dog home and had been rehomed before. We started out by isolating her from the other cats in our home doing a slow introduction. We let her out after a few days for short periods of time to interact with my 3 other cats. Everything seemed to be going good until she started chasing one of my cats, this cat that she was chasing is normally very subdued but doesn't mind playing with the other two resident cats but this time the hair on her back and tail were all sticking up like she was afraid or angry.
I separated the new cat from the others and let them calm down. After a little bit I let her back out while the cats were playing with some feather toys. The new cat started to play along with everyone and seemed to be getting along with them. And then completely unprovoked the new cat whacks my one cat in the face and goes after her.
I've separated them again by moving the new cat back into a separate room with food and her litter box. Has anyone encountered something like this when bringing new cats in to a home. I hate that I have caused undue stress and tension on my resident cats but I can't help but want to give this new cat a chance. I hate the idea that this new cat has been given up time and time again and I would love for this to be her forever home. Does anyone have advice to make things go more smoothly and help everyone get use to everyone.

Thank you very much for rescuing another cat.

This is very common.

The introduction process should be done at a slower pace. It can take anywhere from a few weeks all the way up to a year at times. Here are some links to help.

http://www.thecatsite.com/a/the-ultimate-yet-simplified-guide-to-introducing-cats

http://www.catbehaviorassociates.com/a-simple-little-trick-to-use-during-new-cat-introductions/

http://www.aspca.org/pet-care/virtual-pet-behaviorist/cat-behavior/introducing-your-cat-new-cat

http://jacksongalaxy.com/2010/10/01/cat-to-cat-introductions/

We really want to go through the process slowly so that no cat feels at risk or threatened. So we try to associate the cats with good things (food, play, etc). If each cat feels like the other cat is not a threat then it is more likely they will get along. We do it through scent at first then visually with barriers then eventually in an open area. The desire is when we let them in an open area they already "know" the other cat(s) and don't feel threatened by them.

From what you wrote I don't see any reason why they all will not get along at some point. Everything you experienced is normal and honesty expected if the process is rushed. So please do not worry, just take it a bit slower and I think things will be fine.

I am happy to answer any questions you may have and will be here for you throughout the process for as long as you might need advice. I am happy to help your new cat stay in his forever home.

Thankvyou for the advice I will certainly follow it we already love our new baby and I couldn't imagine having to re home her again

You are very welcome. There will be ups and downs but I have found that it works almost all the time. It can take a bit of time (some are faster some are slower) but the result is usually success.

I am happy to help you throughout so please feel free to ask anything. There is nothing more I would like than for her to have found her forever home now.

Thank you so much for caring about her. I'll be here for you all anytime you need me.