A down position would not be more submissive than a sit or any other command obeyed. If a cavalier won't stay down, it is because it isn't understanding what is wanted, and our own lack of conveying a clear message, hence the dog will tend to pop back up. Unfortunately the very subtle and complex issues of dominance and submission and the language associated with this area of dog behaviour has been appallingly oversimplified by the popular TV trainers in particular and many books, and carried into areas it just doesn't belong, IMHO. The more I watch professinal trainers work with dogs, the more I feel this is true, to the detriment of our relationships with dogs. I think a lot of dogs would be happier and be trained faster and better if we all simply dropped the whole notion of dominance and submission from our brains and vocabularies and left them where they belong, with the canid scientists.
Dog trainers will always say it isn't the dog that needs training, its the owner. It actually takes a lot of work to learn how to communicate effectively with your dog -- all of us send mixed and confusing messages so frequently -- something I have gradually realised over time even when I was SURE I wasn't (but I hang around too many professional trainers for this pass unnoticed! :lol
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Often we are not consistent in our tone of voice, even in what we say; we repeat commands several times so that 'sit' means nothing to a dog; it is waiting for a 'meaningful' command like 'sitsitsitSIT!' which WE have taught the dog is the 'real' command through our own impatience and cluttered way of communicating.
I actually think it is easier in many ways to train a deaf dog as we are forced to give a single very clear hand signal rather than out idle chatter which must really confuse dogs. Plus we often do a range of body movements with a spoken command, not a consistent movement, and the dog can get confused by those -- dogs tend to watch body language more than listen for commands.
I've actually found cavaliers, including a deaf older cavalier, really easy to train. They seem to always love to do anything that is fun and rewarding (hence why correction based training tends to defeat a cavalier and intimidate, not promote learning). But it is one thing to get the initial vbasic command across -- and quite another to have this elicit a consistent and reliable response, especially a down stay, which takes ages to build up to longer and longer downs. You need to work in one then 5 then 10 second increments and onwards tilyou can get a downsty until released. Hard work!
If a cavalier seems really stubborn, owners might want to might check its hearing, especially in any dog over about 5. Also try reteaching commands along with a hand signal and see if the hand signal doesn't work far better.