Should the owner be in training with the dog?
Absolutely, positively YES!!!! There's no use in training a dog or puppy if the owner and family members aren't also trained to work with the pet. Remember, people and dogs have frequent communication problems, because we speak English, and dogs talk "body language."
Most bad habits dogs have are ones they either 1) got away with due to ignorance or indulgence by the owner/family, or 2) got trained into accidentally &/or unintentionally by the owner/family.
Unless the owner and family are taught how to properly interact and communicate with the dog or puppy, and use his newly-learned obedience commands appropriately, all involved are going to be continually frustrated with the problem of "what you thought I said was not what I meant." Like young children, dogs are masters at figuring out very fast which people they can, and can't, manipulate. Do you want to stay in the ranks of the manipulated?