I was actually thinking of suggesting a bichon (frise). Here's a website that may help you search:
Hypoallergenic Dogs | List of Hypoallergenic Dogs | Hypoallergenic Dog Breed Information
You are able to enter your responses to certain traits and it helps narrow the search for you.
I'd agree with nanahas3 as well. If you are truly invested and you've taught your children well how to treat and respect animals, I believe you can have a small dog. My children grew up around our first sweet boy Charlie (he was our "first baby) and even helped us the last few years care for him as he became elderly and more fragile. When the time was right to welcome some new furbabies into our hearts and homes, I didn't hesitate to get yorkies. That's just my opinion.
Good luck with your search and I hope you find the dog that's the right fit for you and your family
