Hello OP, good to see you back.
Did your son move away for his time at university? Does he have that experience of living independently and of appreciating your comfortable home when visiting?
It sounds as though he takes your home, funded by years of your hard work as an adult, completely for granted. Yet he couldn't fund anything of the sort for himself. Of course it's lovely that he can feel 'at home' when he's there and you'd always want him to want to visit you but that's not the same as having a never-ending right to live as your guest.
The other thing that really struck me, is that you only seem to mind the impact of your DS's behaviour on your DH, not on you. Why would you not mind being disrespected, lied to (about the tasks he's 'going to do later') and treated effectively as a servant, by your DS?
He doesn't have anything like the concern for your wellbeing that you have for his - or apparently much concern at all.
It must be really stressful for your DH, seeing you being treated so badly, daily.
Do think too about how your DS is going to behave with a future girlfriend or wife. Becoming habituated to 'letting someone else be the grown up' and to seeking to get away with doing as little domestic work as possible, is not healthy and will limit his options (it's not attractive behaviour) and his chances of maintaining a successful relationship.
You really would be doing him a favour, as well as your DH and yourself, if you set out and enforce some house rules - or help him look for a room in a shared house as an alternative.
It must be stifling and frustrating for him not to be able to invite friends over when it suits him, at his age. But, if he and they don't behave like proper guests, of yours and he's not pulling his weight as an adult member of the household, so be it. I'd be flat / shared house hunting in his position!
If he slinks off to his dad's house, people will think either nothing, or that he's rather lazy and undignified. They'll probably be secretly congratulating you for firming up your boundaries.
The other thing that emerges from your recent post (and I may well be reading this into it from almost nothing) is some idea that your son might feel he has some choice about whether your DH lives with you or not. As if, because DH seems grumpy and moody, to him, this is some challenge to a DH's right to be part of your - you and DS's - household. You're an adult. DS is an adult too. That sort of jealousy and proprietorial attitude to you would not be healthy.