Quite honestly it sounds like he is behaving badly at home. You are not a doormat, you are his guide and allowing to behave as he wants at home is rather weak, not much fun for you and the rest of the family and a fairly massive sacrifice just because you don't want to risk a breakdown in communication.
We have been through difficult teen years and have managed to have clear boundaries while maintaining good communication.
If he doesn't do as you ask and you just sigh, why are you surprised if he doesn't do as he's asked at school?
Be kind, maintain humour, respond openly to questions (i.e. say, gosh, did he? What happened then? How did you feel?, rather than god, that's awful, the teacher must have been furious). I would recommend how to talk to teens so they listen and listen so they talk. You can acquire the basic idea in an hour's reading - it helped me a lot. Do not get angry and shout, do not overreact, give yourself time before you impose a sanction, think it through.
Our house is rather transactional - no, I'm not taking you to x/giving you y or lending you z because you haven't emptied the dishwasher.
There are things you can relax on and things you need to maintain. One of the things you need to fight for is respect for you and the rest of the family. There will be slips of course. If you tell him to go and do something and he does it in bad grace, swearing under his breath, let it go.
Ask his teacher to let you know when he has been disruptive in class and then set in place a clear sanction. For example, we had a system where a negative report from the teacher meant no computer time all evening. Every time.
Your DH sounds like he is being very soft and lazy about parenting him. I think you need to realise that your bright, popular son has many strong assets that will serve him well in life, if he is guided and taught how to behave by you.