clara, I read the OP's post differently: I think she was trying to hurry him into the shower because he insists on one before bed and it was already after midnight, rather than that she was insisting he had one.
That said over, I think you may need to back off. This is going to sound contradictory, so before I explain, I will repeat that your son's behaviour does sound worrying, and I would also be concerned.
However, one of the very most difficulty parts of parenting a teenager is that at some point you have to confront and accept your own powerlessness.
When they're little, you generally get to decide what they do. When they're adults, you obviously don't, even if you can see they're making terrible mistakes. Somewhere in between, you have to make the transition from one to the other, and that often seems to start when boys are about 14.
Lots of kids fight and rebel, which is a nightmare at the time, but effectively 'helps' this process, as they become more independent and you give up control. It struck me that lots of parents fight to get their 14 yos into bed before 2am (I know I did!), and to eat properly, etc... But they tend to be noisier battles, somehow - more 'in yer face' than your DS is being...
Because of the circumstances, it's very hard (for you, him, and us) to separate out what might be 'normal rebellion', from what is worrying... It sounds like your son is involved in a different kind of 'rebellion' from most teens (a more passive-aggressive one perhaps?) - but a battle with you none-the-less...
So, I reckon it's worth trying to remove yourself from the battle, because that will show you which bits are about a struggle for independence. If you stop exerting control over him, even just for a bit, then you will see what he can control for himself, and what he can't.
So, if I were you, I would try a new tactic... I would say quite straightforwardly to him "OK, I can see you think you know what you are doing. I'll back off and give you a chance to prove to me that you're responsible enough to look after yourself without me hassling you. I'll back off for a week, and if it works, and you don't get ill, and you get to school and continue to do ok, and you still do your chores/sports/whatever, then I'll stay backed off. I am still worried about your health, because I know from experience that not eating and sleeping properly makes people ill, so if I think your physical or mental health is at risk, I'll step back in... but if you stay healthy, I'll let you make your own decisions... So, I'm going to stop chasing you to go to bed: when you go is up to you, and if you're late for school, you'll need to deal with that. I'll stop chasing you into the shower, but I don't want to be woken in the middle of the night, so if you haven't had one by X o'clock, you'll have to leave it til the morning... And I'll leave it up to you what you eat/how you exercise/etc... Is there anything else you'd like me to back off from..."
This is very different from 'giving up' on him; this is not you 'doing nothing': this is giving him a chance to prove he can take responsibility for himself, since he's showing you very clearly he doesn't want you to control him.
Of course I might be wrong. Of course you know your son better than me. But it seems worth a try. And your DS and dh are right: if your DS doesn't want counselling, then you can't make him have it, so your options are v limited.
These years can be hugely stressful, and it sounds like you're feeling the strain already. I echo the advice to get some counselling for yourself, and to look after yourself in other ways. I'd emphasise the importance of this, in your particular situation, where you are worried specifically about your son looking after himself, because you need to be sure to 'show him how it's done', rather than unintentionally showing him self-neglect.
Blimey, sorry, that's a bit of an epic! I hope at least some of it makes sense and is useful... :)