I'm feeling better after reading everyone's reponses.
My heart really is set on a Yorkie. I have been wanting one for years, but the situation was just never right for what I believe (and have seen confirmed here) is a huge commitment of both time and money.
I'm guessing that the basic consensus here is that as long as the children are trained about the dog and how they should/shouldn't interact with him/her, we should be ok. Am I right?