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I think obedience training would be a good idea. I never went to a trainer with Sadie - financially it wasn't possible and she was naturally submissive so it didn't seem necessary. Fortunately the only problems I've had with Sadie are things that make cute stories but I do believe from what I've read over the years that dogs, submissive or dominant, are happier with a solid social structure. I think it would have relieved some of Sadie's anxieties if I had been a better Alpha but I always gave in to what I thought she wanted - little things that seemed harmless but probably signalled to her that hey, there's no one in charge in this house!
I think the most important thing to get out of obedience training is how to be Alpha - and that's not a lesson for the dog. I know at least for me Alpha behavior does not come naturally. Good luck!