The shampoos you listed are pretty strong. Dawn shouldn't be used as a regular pet shampoo (though some people swear by it in a pinch for getting rid of fleas). And people shampoos (t-gel) have the wrong pH balance for dog skin. When the acid mantel of the skin is thrown off and the skin is stripped of oil, it sends a signal to the body that it should actually be producing MORE oil. It is actually possible to bathe a dog too much. And if the acid mantel of the skin is constantly stripped, it leaves the skin more vulnerable to fungal and bacterial infections which can stink.
The first thing I would do is take the dog in for a complete check up. The source of the breath odor could be tooth decay as already mentioned here, or it could be a sign of digestion problems.
Skin irritations can also be a sign of food allergies. I don't know much about Royal Canin other than there are better foods out there.
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