There is a type of personality that loves to battle when they think things are equal because they believe they can win by force of will. My niece as this type of personality with many knock down drag outs with her mother. My brother didn't accept that type of treatment and as the result, he had fewer arguments. An example is one time she insisted on slamming the bedroom door. After being warned not to do it several times, my brother removed the door and kept it at work for several months until he was comfortable the the attitude improvement.
Both of you are adults, they are the child and are living under your roof. You must agree what is acceptable and what is not and if they fails to live up to expectations, they should pay the price for their actions. The difference between a child and an adult is a child requires guidance to do the right thing and an adult doesn't. As long as they behave like children, they should be treated as such as at their age, they should know better.