My children were 1 and almost 4 when I got Twinkle as an 11 week old puppy and I've never experienced any problems. We have rules such as sitting on the floor and letting her come to them if they want to play and not picking her up (although they'd have trouble - sh's 8lb now) and I dont ever leave them alone together.
I'm about to do it all again with a new puppy and I'm confident it will work out well.
I think it benefits children to be raised with animals (with adult supervision of course) because it teaches them to love and respect them.
I suppose its different with dogs in rescues because sometimes the full history might not be known and it's always better to be safe than sorry.....it would be horrible if a child got bitten because the dog was frightened of them thanks to a past incident. Also, I think some rescue dogs might need the kind of attention you can't always provide if you have to children to care for as well.
I wish you lots of luck in finding your perfect yorkie
xxx xxx