Training question??

[Scooby4]

This is a sign of submissiveness on the dog's behalf. My dog Shaggy did this obsessively when first adopted. He might have been abused prior to my adopting and had really bad submissive behaviors. He wasn't even able to play with toys!
This may sound "cruel" but this is how I handled the problem. He still does it to a degree but only about 25% of the time. My first step was to NOT pet the dog when he "rolled over" and exposed his belly. I would instantly ignore him and NOT touch him until he got back up. I still do this till this day for reinforcement. My second step was to get more "aggressive" for a time period. Whenever he rolled over, I would promptly grab his tail (at the base) and this front paws/front area and FLIP him back onto his feet! Then I would say good dog and pet him.
I did have to "flip" him for a few months until now he is completely able to understand he is NOT going to get petted until he is on his feet. Now I do NOT have to do this at all. He still rolls over but when he sees I won't touch he comes back up. I will admit I do on occassion rub his belly anyways. It's just to let him know that I love him.
Remember, you are ALPHA dog. Dog's like "pecking orders". The dog acting submissive means that his pecking order is much lower than the other animals in the order. This isn't a bad thing and should be recognized. NEVER try to make an "alpha" dog out of both of your dogs. They will fight!

[Dixieland Dancer]

I'm glad the board idea is helping along with changing the command. Using training aids such as the boards has helped many competitors in obedience fine tune and correct behaviors.

I like the boards and positive retraining using a different command rather than ignoring and flipping the dog back over as suggested above. Yes, it does sound like the dog is exhibiting submissive behavior by instantly rolling over (especially if the dog was never formally taught that behavior) but by reshaping the behavior with a new command and training aids such as the boards, you are building confidence in a dog that obviously needs it instead of ignoring it.