I would like to get a small dog that would be suitable for two primary school-aged children. Ideally it will be their shared companion and they will do training and hopefully most of the brushing too. I will probably keep the dog clipped in a short pet-clip. We already have a dog - a standard poodle who likes the kids, but is clearly my dog. She doesn't really cuddle up to the kids and is too strong for them to walk her safely on-leash. Also, my poodle takes up too much room to be a snuggle-up on the bed companion.
So, our most desired features: small, affectionate, relaxed, not too frail to live with a cheerfully bouncy poodle, easy to train, non-shedding. Would either a havanese or a miniature schnauzer be a good fit? Would you suggest something else? (We don't want a miniature poodle, one poodle is enough.)