I think it is good that you are taking these things into consideration before getting your next dog. I personally love love love Yorkies, well, I think I love all furry babies, but Yorkies are truly amazing. I love their look, their intelligence, their 'amazing desire' to BE WITH us...they don't care where.
I didn't seek out my first purebred Yorkie, rather, I got him when he was 14 months old. He was given as a gift from one adult sibling to another adult sibling...who had a 95 lb, 1-yr-old bulldog already...so not a good fit, even though the kids were older. The bulldog and the Yorkie could not be 'buddies' and/or left alone together due to the difference in sizes and their ages and with both parents working, so were separated most of the time. Don't get me wrong...he is an amazing boy, my little love bug, has a great personality and wonderful temperment, and they did a wonderful job with him for his first year.
My girls are fantastic, too, very sweet and well socialized, and are great with kids they have never met, but my boy...who is the sweetest, most lovable boy, and a prissy mommy's baby as well as protector OF mommy and enforcer FOR mommy...was great with all kids UNTIL one boy tormented him by sneaking around him and me, and hiding and jumping out and wouldn't come to him and meet face to face, or pet him, etc. Now, I am extremely careful when children come around him because I worry he might 'sense' some 'evil'
intent on the part of the child and I keep my hand between his muzzle and the child at all times. I also hold him so I feel him if he tenses up when children are around and get him, teeth especially, into a position where he could never hurt a child or adult. He has yet to DO anything but watch 'suspiciously' and 'distrustingly' and make little 'growling under his breath' noises, and some barking, and the kids, and adults, pet him and he does nothing and doesn't tense...but I refuse to let down my guard, knowing he was 'soured' to children by the behavior of one young stranger.
I had a Yorkie-Poo mix that was abandoned as a tiny puppy many years ago, and he was raised with my little sister...a toddler. I was a very young teen/pre-teen at the time. That boy was never harsh with children and could be completely trusted around them. But, much as I love the little purebred Yorkie boy I have now, I would NOT feel comfortable with him being around strange young children immediately.
There are plenty of people here who can provide a great deal more info about Yorkies and young children. These are just my experiences.
Good luck. I am sure you will find a new fur baby that fits into your family and love you for his whole life.