She is very young, so she should adjust quickly, but do give her time. With the kids being that young. Let her be your dog, but she does need to respect the kids. My Yorkies sometimes bark when my teenagers come into my bedroom because that is what dogs do. They stop barking when they see who it is.
Watch the puppy closely with the kids as they are too young to be left alone with the dog and not able to be responsible for a dog at their age.
I do believe that they can happily live in the same house and the kids can play with the dog (while supervised).
I took in a 9 year old Yorkie and it took him several months to fully settled in. A 6 months old puppy I would say should settle in quite a bit quicker. I would definitely give her a few weeks to get comfy. Help the kids gets used to her. She will want to play soon enough and then you can show them how to play with her, like throwing a toy. She is still a puppy and could accidentally bite them in her excitement. My 9 months old and almost 10 year old Yorkie sometimes nip me a little while playing, so be sure to show them how to play as safely as you can. If the puppy does bite them even slightly they should be taught to yip sharply or in a high pitched voice say OUCH! and the puppy should know she hurt them on accident.
Good luck! I hope she adjusts well and ends up being a huge part of your family!
__________________  It's raining Yorkies here! LOL Teek  ,Rowan  , Raksha (Grand Puppy)  , Raelyn |