Can you send your dog away to be trained?
You can send your dog away to be trained. There may be some benefits, but some of the major elements of dog behavior are not addressed by doing it this way. Consequently, it may not be the most effective way to get the dog trained.
The most significant part of your dog's behavior response is based on his relationship with you. His relationship with an external dog trainer is another thing altogether and is not in play at all when it's just you and your dog.
In any given situation, the dog is reacting instinctively to his relationship with another person. You, as the dog owner, need to understand how that works, what is happening between you, and how you can control it. You don't get any of that from sending your dog away to be trained by someone else.