shih tzu's. lhasa's, bichon, all are non shedding, and yu can usually find these breeds in rescue. They love to play, but don't require a strict exercise commitment, cuddly, and strong enough for kids. Grooming is high needs. but they don't shed.
I have a shih tzu lhasa cross and it is great for little kids, he is small, but sturdy, his legs are probably 3 times thicker than a poodle or a pom. he can keep up on long walks, and likes to snuggle, and he is a rescue!
poodles are fragile, and can be nippy when they are 'hurt' I don't recommend them for small kids, or poms for that matter. go meet a lot of dogs and let one pick you, take the kids, you will find the new buddy!