The best nonshedding small dog breed on this list is a Maltese, but they are tiny dogs and if you have rambunctious kids there can be injuries. I did not get my Maltese until my son was about the age of your youngest, and he still injured the dog playing with it. You may want to get a larger dog if you have small kids, but there may not be as calm a small dog as the Maltese.
An adult dog is much more suited to being alone during the day. A puppy needs to go out more often, gets more bored, and may develop behavioral problems because of that. Take a look at Petfinder.com to see if you find an adult dog that suits your needs.