When Our Blessed Lord walked the earth, He said that "The scribes and the Pharisees have sitten on the chair of Moses. All things therefore whatsoever they shall say to you, observe and do: but according to their works do ye not; for they say, and do not. For they bind heavy and insupportable burdens, and lay them on men' s shoulders; but with a finger of their own they will not move them." (Matthew 23:2)
He was speaking about the wicked Pharisees, who stubbornly and maliciously insisted that Our Lord was bad, even when he rose people from the dead.
But a better example is when Our Lord was silent before the Sanhedrin, but he spoke to certain individuals (Pilate, the Chief Priest) out of respect for their authority.
Moral of the story: being a bad guy doesn't instantly mean you LOSE ALL AUTHORITY -- it just means you no longer have a right to be obeyed or followed in every case. It means people have a higher cause, which allows them morally to NOT follow you.
If I got into a bad phase and stopped going to Mass, committing sins all the time, yelling, being generally grumpy because of my new disquieted soul, and being a total ____, would I lose all authority over my children? No, but there might be some commands given that they shouldn't obey -- since in this hypothetical case, I'm obviously not thinking "God first" anymore. Also, it might be smart for them to not hang around me any more than absolutely necessary. They would still need to keep a certain respect, but prudence might require they don't "stop in my office" for fun/social reasons like they were normally wont to do. Because in this hypothetical "Matthew-gone-evil" scenario, they might see something bad on my monitor, or learn new swear words from my mouth.