He looks terrific! What a doll baby! You are surely his angel.
Could you try to teach your children to quietly and slowly approach him with a treat and see if he will accept it from them? If he does, maybe you could keep working with the treats to get Teddy to see the children more favorably? I really think the quietly and slowly is key. And only when you can supervise.
If that doesn't work, get the kids their own yorkie puppy!