Roles of Mothed and Father in TSG

We have discussed the roles of parent and youth in our family, but not necessarily the differences between mom and dad, specifically when it comes to TSG. The book, Roles, helped a little, but it is still murky. Ephesians has some discussion of the roles of parents and husband and wife, but with our roles TSG we have been getting into some heated discussions. I am home all day, every day with the kids trying hard to do TSG while homeschooling and running kids to so many activities and then, my amazing hard working husband comes home maybe 2 hours or 2 minutes from bedtime and, biblically, I am suppose o led him lead the household after I have been leading it all day. I try to help him remember to keep a calm voice, face and body because after a hard day at work the struggle is real, but he sees it as undermining his authority, while I see it as trying to protect relationships. I will remind him the order of consequences and same- I am interferring or he accuses me of treating him like another one of the kids with my reminders. He now has said he is handing the leadership reigns to me. That a company only has 1 CEO for a reason and he has elected me, but should he be the CEO in TSG, biblically speaking? I told him also that unity starts with us and since our vision is one of being unified in Christ and as a family that that starts with us and does there have to be a CEO? Can’t we do it together and help each other? He says “no”. There are no companies with 2 CEOs. I really see this as a role issue between the 2 of us and asked him to think about what he sees his role in this family is and I can already tell you that one thing he will say is he sees me in charge of parenting and he will defer to me and that IS unity. Him supporting me and deferring to me IS unity. My brain is really struggling with I see that I kind-of am in charge of parenting and discipline, but is that how it should be? Are our roles biblical when it comes to parenting and discipline because of how much time I am with the kids vs him? I honestly did not see reminding him of the steps or order of consequences as “parenting” him, but am I stepping into that role when I do that? We could really use some guidance on roles of father and mother and their differences. Thank you. I am living this and sleep deprived so having your perspective as expert and outsider is much appreciated. There are a few questions in here, but they all point to role differences of mom vs. dad.