I would send him to animal control.
Sorry, but she's risking her kids being bitten in the face or permanently damaged by keeping the dog.
Some dogs ARE just biters. Not all dogs are able to be rehabbed. Most, yes. But if she cannot contain the dog and cannot find a rescue willing to take on a biting dog, she needs to send him to animal control or have him euthanized herself. Every day she keeps it in the house with her kids, she is being irresponsible.
It's possible the dog could be rehabbed with a professional trainer. It's equally possible that one of her kids will lose the use of one or more fingers, or have their face torn open before she can get the dog trained. I don't care if it's a toy poodle, it can do a LOT of damage before she can do a thing to stop him. He's biting for several reasons, and it will only escalate.