Congrats on deciding to get a dog for you and for your kids!
As already mentioned and IMHO it would be easier on you AND the kids AND the dog if you could choose a somewhat older dog in a small but not fragile size. Just imagine to have another baby there b/c that's what it's going to be like only that this baby can be fast in pooping and peeing on the carpet and in places where you really can't get to easily...
Maye you could look into rescuing a dog that lives now in a foster home where you could be sure that he/she gets along with kids, walks nicely on a leash, is potty trained, does not throw up in the car, doesn't chew up your furniture, shoes, your kids toys, isn't allergic to certain foods, is already spayed/neutered, has all the necessary shots, a clean bill of health (no LP, Liver Shunt etc.) and has all excess puppy teeth already removed. Those first 2 years of a Yorkie puppy can be quite expensive and you would need to keep an eye on the puppy and the kids
all the time and when you think that you get a quiet moment b/c the kids are asleep then for sure the puppy needs you for something...
Good luck!