Well, it does happen sometimes, even with the most careful and best-handled introductions. It's happened to me, so I know how hard it is...especially since you didn't go looking for another cat, it was a kitten rescued off the street by your wife and kids. Sometimes you just can't make it work, especially with a resident cat who's been queen of the roost for so long. If you feel that you've reached your limit, it's time to start considering the options.
So what are
your options? First, you can rehome the cat yourself, by asking around friends, co-workers, neighbors, and relatives to see if they'd be willing to take in a lovable black and white kitten. Ask your vet if he will help you out in placing the kitten, vets often know of people looking for animals. Second, go to the "Cat Chat" forum and read the thread on No-kill shelters/rescues to see if there's one near you that has room (also, try a web search on your town name and "no-kill shelter" or "cat rescue"). Your last option should be to take the kitten to a pound or shelter that euthanizes on a large scale...they're crowded enough already, and it would be a sad end for the kitten to go from a family to a shelter, only to be euthanized in a week's time.
I know this is not a time when everyone is thinking clearly, but honestly, it will be easier to live with the situation just a little bit longer if you know that you're working on finding the best home for the kitten...it really does make it a lot easier to deal with it if you know for sure that you're making a plan...it helped me immensely knowing that we had a new home for the dog, even though he remained here for a week while his new people got ready for him...my cat was absolutely unbearable to live with, but just knowing that there was light at the end of the tunnel helped me get through that week.
Edited to add: Try here for a starting point, and ask shelters that don't have room if they have any suggestions after you explain the situation. Most will be happy to refer you to other shelters and agencies. A note, though...Florida shelters have been pretty overloaded since the huricaines, so it may take some legwork or spending some time on a waiting list...keep trying.
Also, try the "cats in need" forum here.