God bless you. In order to home school, your son will have to take you seriously, and yet he can do that and continue to be strong willed and a leader. God certainly needs souls with strong wills and leadership abilities to follow His Will! You are on the right road, understanding that you should guide or discipline your son rather than punish him.
If he listens to his father, then he is capable of being obedient. And if he listens to his father, then you need his father's support. The three of you might want to sit down together and discuss this situation in concrete terms that a seven year old can understand. Your husband needs to get the message across to your son that he must be obedient to you in day to day circumstances.
Perhaps your husband can also help you to understand your son's style of leadership. From the information in your question, it appears that he favors authoritarianism and structure. Try to make the school day structured to fit his style if that is his leadership style. That means starting at a particular time and finishing at a particular time. It also probably means that your son would be more inclined to adapt to the school day if he has some input into what you are doing and when it is done. Give him some material upon which to apply his leadership abilities, and you can certainly challenge him as to why he makes particular decisions, as in "Why do you think it best to do math before lunch rather than after lunch?" Make him explain his decisions. Do not crush his desire to lead, but try to channel it in positive direction and help him to think through his decisions.
As to corrections, his insistence on corrections may be arising for different reasons. You will need to figure out why he corrects you. Is he using corrections as a means of defiance or procrastination? You may try ignoring his corrections or simply responding with a "thank you for your comment" and then moving on. When possible, you want to avoid creating a conflict for him to react against, but if you absorb the conflict, he has nothing to struggle against. It's a type of verbal judo or tongue fu, which law enforcement and other professionals use to prevent situations from escalating. Learning more about verbal judo may help you understand how to gain cooperation from your son. Here is a link with some quick tips: http://www.tonguefu.com/media/articles/ten_tips.html
Is he strongly literal and insistent on the truth with no deviations? Then he is probably task and detail oriented. This trait is wonderful for accountants and other professionals! But he needs to temper it with charity. I love the story of St. Thomas Aquinas who allowed himself to be corrected (falsely) when he was reading. When he was asked why he did not correct his corrector, he replied that it matters very little to God whether we pronounce a vowel long or short, but it matters greatly how we treat His subjects. Perhaps you can both reflect on situations where he has been wrong and how he would like to be corrected. And then you can discuss how you would like to be corrected when he believes you have made an error.
Your son may not outgrow a strong will, and let's hope that he does not outgrow being a born leader. But he needs to learn to use these traits for good in harmony with God's Will. And you can help him! Pray for him and with him, and communicate with him and with your husband about this matter. And have patience with yourself and with your son.
May God's peace be with you.