Aww she looks exactly like my LUCY. We have small children too and I tell ya,you just always have to be supervising them at all times with the animals if they don't know how to behave around them. It is a lot of work in the beginning but they get it. Lucy is one of my kids so I want to make sure she too would not be harmed. My girls learned early on to always be gentle and treat the animals with respect. I have always told them if they want nice animals then you have to be nice back and remind them how much we love her etc etc....I dunno, that is always what has worked for us?? but I realize every family/kids and situation is different.
GOod luck to you and also I commend you for even taking this step of being open to finding her a home if things don't work out or you just can't take anymore. Not every family is suited for a small dog etc....thank goodness so many adore Yorkies! Good luck!