First off, I sympathize with your situation. Second, you have come to the right forum for information. Third, I'll put my 2 cents in regarding your problem (even though I'm a relative newcomer to this forum).
I'm presuming you got your Yorkie as a puppy ? That would probably make him 6-7 months old ?
From everything I've read, the cage/crate is supposed to be a place where your dog FEELS SAFE, and GOES IN WILLINGLY. Of course, this requires time, patience and training to achieve (much like everything else involving a Yorkie). Otherwise, he's gonna cry, whine, chew, etc. because he wants to get out to be with you, where you are !!! These dogs are terriers, which means they can be feisty, independent, willful, and yes, stubborn, but once they are trained, they are a joy, very affectionate and loyal; they will bond to you very strongly once they trust you. The downside is that it does take more time and patience than a lot of other breeds. Potty training can also be notoriously difficult.
One of my neighbors had bought a Yorkie puppy, and while she and her family loved the dog, quickly she became "overwhelmed" by him, as a matter of fact, it sounds as though you and she had many of the same (and I would guess common) problems. My neighbor has two small children under five, both she and her husband work, etc. Finally, she gave her dog to her sister, and everyone has been happy since (my neighbor still has her cat).
I'm not here to judge, but perhaps the Yorkie is just not the dog for you. In my opinion, unless you have the time and patience to devote to them, it is unfair to both you and the pet to continue in a situation where obviously neither of you is happy.
I must disagree with you regarding a blanket "breeders destroying the breed" statement, otherwise, why would there be so many happy Yorkie owners ?
Every dog has a different personality, but I think most of the time, problems stem from inadequate training.
Please understand that I wish you the best of luck. If you want to keep your Yorkie, get a good, Yorkie-specific training book, and follow through with a training program. If not, please find a good home for him with someone who does have the time to devote to him.