He thinks he is doing you some extraordinary favour by covering his genitals in a house where there are two girls old enough to notice, and a wife who is repulsed by the sight of it all flapping about?
He is seriously up himself and I stick by what I said earlier. There is something, perhaps two things really, really wrong with him.
That phrase 'his house' -- don't dismiss it. It deserves much more weight than you are giving it.
'I don't think it is fair to say he is abusive - I really don't think he is. Yes, he can be petulant and sulky at times and he isn't empathetic. But I don't think his lack of empathy is down to malice - he is just someone who struggles to see anyone else's point of view. '
You are judging him by what you assume are his intentions but you should be judging his actual behaviour, his words and his actions -- because those are the things that are having an effect on your girls. Those are the things that will shape their view of men, of relationships, of their own rights within relationships, along with your behaviour and actions, and not your intentions. How they behave when they are adults, and their basic attitudes to themselves and to others are being formed now by what they see and hear and feel and not what you intend or what he may (or may not) intend.
He is an adult and so are you, and if you are able to see how your actions come across, or anticipate how they might affect others, then why do you not expect him to do this?
You are allowing him to get away with behaviour that is actively harming your DDs if you let him be a sulk, moody, petulant, and lacking in empathy, a man who struggles to see anyone else's pov. Does anyone else in the family get to behave like this?