I suggest reading a parenting book from the Love and Logic series. Foster Cline is one of the others. L an L also has a eb site describing their "style."
Their logic is based on providing consequences that teach right behaviour instead of punishing wrong behaviour. When I focus on teaching, I'm able to find consequences that are related to the behaviour I want to change. I started with the simple consequence of sending a child to their room because I don't want to hear that language or be around that behaviour.
At first my grandchildren refused to go. I just stood there looking at them (the "evil" eye, without saying anything. All activity in that room stopoed until they left. TV turned off ignoring everything the child said. Projecting calm expectation they will leave. My daughter and I started this when they were young. They mostly automatically go to their room when given that straight on, this is not acceptable look. At first, one of their parents guided them to their room.
Your son is too big to guide. I would accept him leaving without insisting he,go to his room. I suspect, you will have to spend 5 minutes or more staring him down before he leaves. The purpose of doing this is to teach him you will not accept such behaviour and you will not let him engage you in a fight. Once we fight with a child we lose.
We cannot preach our child into obedience. When we take away things unrelated to the misbehaviour, we encourage more anger. That is not to say never take away things. Just remove things when they are related to misbehaviour.
Sending them to their room or out of your presence is not a time out. They decide when they are willing to be respectful and return to your presence.
At a time, when things are more mellow, I would ask them what they suggest you do to help them be able to show respect. Again, don't get caught up in his anger which is his way of taking away your intention to teach. If he's willing to have a reasonably calm conversation, talk about your expectations of respect.
Along the way tell him you recognize how difficult it is for him to be in a home that has different expectations of him than you do. Be careful to not criticize or judge his father. He will defend his father. Remember that your goal is to teach him how to behave in your house.
Teaching in a mostly confident, calm way is different than your usual way of responding. We become angry when we feel powerless. I suggest he also feels powerless. He is powerless to change the conflict between your expectations and his Dad's. He will fight back until he realizes that you will be consistent in your discipline. That you, even tho you don't condone his father's influence on him, you accept it as something over which you have no control. You love him and want all of you to be comfortable in your family. Never mind what his father does. You really cannot change his Dad. You are unlikely to change your son with punishment. You have a much better chance of controlling his behaviour with love and logic.
I also suggest you be the one to discipline him. Children are more able to accept a step-parent if they don't discipline in situations like this. It is normal for a child/teen to have less respect for a step-parent than a parent. I suggest that may be why your son is using those words with him. He may also be trying to break up the two of you.
Respect has to be taught. I suggest it would be normal for him to feel you disrespect him.