Gosh, that sounds like a challenging time for all of you.
Several thoughts, probably random:
First, developmentally, six is an "attitude" age. Does it help you to know that what he's doing is developmentally appropriate?
Also, he's expended a lot of energy to keep things together during school, and his reserves are spent after school. Is there a way you can set him up with something where he can recharge his batteries for 30-45 minutes right after school?
Our ds is an introvert, his sister is an extrovert and when he comes home from school, she's dying for a playmate, and he's dying for some down time. It creates a lot of conflict.
Several recommendations for books that might help:
1. The Challenging Child by Stanley Greenspan. It focuses on connection first, and then problem solving, and then consequences. I've used some of those ideas with our ds and dd, even though they're not technically as challenging as the kids in the book. So, while the book is designed for kids with 'issues', I think it can apply nicely to all kids. One thing it recommends is 30 minutes of 'floortime' with the child EVERY day where they direct the play. Ideally both parents in the home would do this.
2. Kids, Parents & Power Struggles by Mary Sheedy Kurcinka. Although power struggles is in the title, it's an excellent overall parenting book.
3. The 5 Love Languages of Children -- what are your son's ways of feeling loved? If there's a mismatch between what you are doing to express love (based on your own love language) and how he wants it, that too can lead to disconnect. The 5 love languages are: Time/Attention, Words, Touch, Gifts, Acts of Service. For our ds, his love languages are: Time and Acts of Service. Dd's are: Words and Touch, and to a lesser extent Time. Mine are Acts of Service and Time. Dh's are Touch and Words. And yes, the disconnect between partners does lead to problems sometimes. Ah, and I just realized that ds and I have the same love languages and dh and dd do. No wonder I'm frustrated more by dd and dh than ds!

Finally, and maybe most importantly, when do YOU get to recharge? I'm a lousy parent when I can't recharge. It's taken me years, but I do need to consciously spend time to do this. I'm helped by the fact that I WOH, so I do get intellectual time every day. But I also need some social time, and it's taken me a while to be at peace with doing Bell Choir every Tuesday night, even though my kids don't like me going out again at night. OK, I'd also like to do choir and a book club, and I don't do those because then I'd be gone a lot more than one evening a week. But one evening a week, for an hour and a half, I'm not a mom, I'm not a professor, I'm just notes B and C (or A and B or D, G, E or whatever).