When you need to describe someone who is difficult to deal with or stubborn, you might use the term "hard-mouthed." However, there are a variety of synonyms you can use to convey the same idea. For example, you could say someone is obstinate, unyielding, or inflexible. Perhaps they are intransigent or recalcitrant, meaning they refuse to comply with requests or commands. You might say they are pigheaded, mulish, or bullheaded, implying they are stubborn to the point of being foolish. Regardless of which term you use, it's clear that "hard-mouthed" describes someone who is difficult to convince, negotiate with, or persuade.