I debated weather or not to respond to this.
I myself have young children. 5 and 8 are my youngest and they are girls. They are extremely careful and I am very diligent with the safety of my lil' Ahi. I know 5 is older than 2 but... I also run a daycare out of my home. I have a 3yr. old, a 2yr. old, two 1yr. olds, and a 6 month old. My lil' Ahi however are completely out of reach of these babies. The only time they can actually touch her is when I am holding her or for the 3 year old she can hold/pet her while sitting on the ground between my legs. They however go home at the end of the day.
If you ask my kids or my hubby for that matter. I sound like a broken record. I keep reminding everyone that Ahi is about... or coming their way. She is NEVER out of my sight. There is no running allowed in my home. We can only do the Yorkie Shuffle.(sliding of the feet) There are SO MANY rules in this house and we all stick to them. So I ask...are you willing to go to this extreme. I don't regret it one bit(neither do my hubby or kids) that we had to alter our lifestyle and routine at home. You may think that this is a bit much but I look at my "dog" as if she was one of my kids. I would be devistated if anything happened to her. My baby girl is definitely worth it.
Just think about it and make the right decision for you and your family. Your daughter can be taught but no matter how much you think she "knows better" kids will be kids. Like a previous poster said kids are unpredictable and I know this first hand. Your puppy and daughter will need 100% supervision. Yorkies are extremely fragile.
Best of luck on your decision and welcome to YT. The people here are great...we are just passionate about our dogs and will give you our honest opinions.