I think you are falling into the trap that so many parents (including myself sometimes) get into, which is trying to win. You aren't engaging in a shouting match (which is to be commended), however you are engaging in a battle of wills with the strong eye contact and body language. You both see it as a contest, and a contest much have a victor. It's the same thing deep down as 2 males from many species fighting for dominance, reasoning doesn't enter into it on either side.
If you continue to engage in contests he is going to get stronger and more defiant. Your relationship could deteriorate and you could end up in constant battles.
What you have to realize is that as children grow up they want more control of their own lives, and if you don't give it to them they will often take it whether you like it or not. There's actually a lot to be happy about with your son. He has spirit, and if he stands up to his own dad he's not going to let some bully take advantage of him! Rejoice about the fact that you have the makings of a strong, confident man in your boy. Realize at the same time that that same spirit is going to make him want to strike out on his own, and take control of his life. He's entering the phase where he goes from being a child to being an adult, and it's natural and good that he wants some control.
Your job now is to help guide this young person rather than trying to control him. Control is out. Throw away the word obey, and bring in the words compromise and cooperate. This means you have to give sometimes, remember it's not about winning, it's about guiding. Give him a bit of responsibility, and praise him for good work and effort. Once he handles a bit of responsibility give him a bit more, and tell him why you're giving it to him. Let him make some decisions, give him choices. If he wants to be treated like an adult then do so, but in increments.
Some parents set up a written contract that states expected behavior on both sides. This sounds a bit legal, but what it really does is provide a framework for you and your child to discuss how things will happen in the future. It helps start a dialog when both sides are fighting. You could use it to set limits on TV and video games, for example, and get him doing chores. If he doesn't do his chores then he could lose video game privileges for example. Most importantly your son must be involved in drawing up this contract he has to feel it is his, not something forced upon him.
If you fight every battle then your life will be nothing but battles and home won't be a good place for either of you. Pick your battles and fight only the things that really matter. Establish some give and take, use choices to avoid arguments.
Most importantly you need to keep your relationship with him healthy. He's obviously trying to get your attention, that's why he's making your daughter cry: he knows it pisses you off and will get you interacting with him. He will keep hitting that button if it's the only way to get you. He's not doing it out of spite or malice, it's desperation! He wants you, and acting out is the most effective way to get you for certain. So, do stuff with him: get a ball and take him to a park, go to a movie, go for a walk. Teach him about life, about how to be a good person. Boys look to their dads to teach them to be men, that's part of what he wants from you.
Ask yourself what kind of relationship you would want if you were him, and how you would like to be treated. Use that to guide your behavior. It's not always easy and you will make plenty of mistakes, but he will recognize the fact you are putting effort it and overlook the mistakes.