It all depends on the yorkie and of course the child.I have 2 kids,my son is 8 and has adhd and my daughter is 5.My son is quite rough because of his condition so we keep him away from Lady who is way to tiny to let him play with her (she is 2lbīs) but he plays nicely with Jess who is 7lbs.My daughter is great with Lady and Jess,she loves them to bits and is no problem at all.
I also have a cat and he loves my babies
Infact,they lay together every now and again and of course they play etc.If your kids are gentle and undertsand that they must be careful,then everything will be fine
Also,you have to watch out with kids because they tend to feed pups things they shouldent eat
My daughter used to slip Jess sweets and other junk food and Jess would get sick..so watch out for that