Firstly, the pet must not be FOR the 4 year old child. There's no way a 4 year old child will understand all the responsibilities of a pet owner. If you want to get a pet, get it for the family, and knowing that YOU yourself will have to take full responsibility over it.
Since you live in an apartment, you can forget keeping large dogs. So, out goes the lab or retreivers. If you are thinking of a dog, get one that is medium or small in size. Since you have a 4 year old, you need one that goes well with children. Beagles make good examples. A cat will also be a good candidate. Try searching around in your local animal shelter, you might find one that's suitable, plus you get to save a life.
No matter what you choose, you have to know that a living, breathing creature will definitely answer to nature's call. Everyday. If you're tired of cleaning poop from a small dog, imagine doing it for a larger dog. You have to be responsible for it, just the same as having a child. Plus, dogs such as the beagle will definitely need its daily exercise. Otherwise, it will get hyper too.
Have you even thought about having your chihuahua trained? Or maybe get the advise of a dog behaviour specialist? Most of the time, annoying animal behaviour can be easily overcome, for example by changing the way you treat it. Try seeking advice before you decide to get "rid" of your dog.