J.J.
I would think long and hard about getting a dog with a young baby. Basically, having a puppy is like having another baby. They require very consistent potty training, or it takes forever. They take time and patience, not to mention they have accidents (just mentioning that because you say you are a clean freak), just like kids.
I agree with the other posters. It depends on the breed. Some dogs are more intelligent than others by nature (I'm fairly certain that dalmatians are the worst, poodles the smartest). Also, be certain that you are getting a breed that is good with children. Some dogs are just naturally aggressive or territorial (terriers are often barky and territorial, and might nip, chihuahuas, while small and adorable, are very aggressive). While these dogs make excellent pets, they take extra time and dedication - especially with the added challenge of having them around your children, who often run and are not particularly gentle to animals.
I highly recommend getting/watching some of Cesar Milan's videos/books (Dog Whisperer) or you can catch him on Nat Geo or Discovery. His website might have some good tips too. Be sure BEFORE you get the dog that it is the best thing for the DOG and YOUR FAM. Kids get awfully emotionally attached to pets and I can imagine it was fairly traumatic to give back the first dog, and to have it happen again would be heartbreaking. Not to mention, the older the dog gets, the harder it is to find them a good home (people typically want puppies). So, do your research, think long and hard about the time committment and possible mess involved. If you're willing to accept all that, then I'd go ahead and get the pup! Dogs are the best and they really can be a child's best friend.
Good luck!
J.