I'm so sorry you are having problems, this is just one of the reasons I'm against dogs being sold in pet store. Pet stores as well as breeders who sell for profit, aren't interested in placing a dog in a home where he fits, they are only interested in selling a dog. A good breeder probably would have refused to sell you a Yorkie, because of the ages of your children. I have had lots of different dogs, and experience in training, and I can tell you that Yorkies are much more difficult to train than other breeds. They also don't seem as eager to please as other breeds, and this can present a challenge to people with limited training skills. The yorkie is a smart dog, and stubborn as well, and I think they are best suited in homes, with a calm stable environment. There are so many breeds that are great with children, and they are docile and calm, yet eager to please. I'm not sure rehoming just one will solve the problem either. Good luck with your decision, but I hope in the rehoming you don't present the dog as easy to train and great with children. You have a responsibility to find him a permanent home, even if you have to lose money. At 4 months old, you have no idea what he'll be like with children. Joey liked kids at 4 months, but he hates them now.
Didn't the pet store have any type of guarantee? A good breeder would have taken the dog back, for any reason. Please don't take this as me judging you or thinking you are a bad person, but it sounds like you have so much going on in your life right now, the yorkie is perfect for a person who wants
more going on in their lives, like the empty nester.