I'm think of taking my dog to the shelter because his training isn't going well.
Why would you take your dog to a shelter because the training isn't going well?
No amount of training will ever get this damn dog to act right.
I know that you're frustrated with the lack of progress with your dog's training, but you shouldn't take your dog to the shelter. Find another dog trainer and try again. Your current trainer may not be as good as you think.
The dog is annoying and I don't want to listen to it whining. I can't stand leaving him in his cage anymore.
You need to at least switch trainers and see if that helps. Just giving up and dumping the dog in a shelter is wrong.