If you are on FaceBook at all, look up the rescue organizations there. There are ususally tons for every breed. You may find one near you. Many of those will even help find transport via volunteer networking.
Lots of people are giving up wonderful family dogs simply becasue they cant afford them anymore. Its a shame, but you may find a wonderful dog there.
I have to say, the whole 'small dogs get hurt by small kids' thing is hard for me to really grasp fully. I know it happens and has some truth to it, but Ive never experienced it. I have a 5lb chihuahua that has never been hurt (had her before I had 3 of my smaller children, and still do, and no injuries yet!) we also have Boston Terriers we got as puppies who have never been hurt by any of my 5 kids. Maybe its more about poor adult supervision tha the kids really being a danger. I know accidents happen, but it sounds like you know what you are doing, have experience and are trying to do the right thing.
Whats worse- a dog being put down due to lack of a specific home requirement, or the risk of a child *maybe* hurting the dog or the dog hurting the child? Sheesh, ANY dog can bite, even the long time family dog everyone loves.
I hope you find your new pet soon- Good Luck and check out FB rescue groups (they are often breed and area specific so you might get lucky fast!)