I think you sound amazing.
I will echo others who say you do need to tell him that his dad is not his biological father. He will ask about who is, but I would keep it as something like suggested up the thread "Travelling and lost contact" type of thing.
I know a few people who were told things like that at an older age and found it much more traumatic than those who knew earlier.
I wonder whether you could do some sort of family councilling as all of you. I think it's important that dad is there so he can reassure him that he is still "Dad" and loves him and doesn't matter. Maybe if you parents went and discussed it first, and then at a later session took him and told him. Then there's someone who can help him then and there with a more (iyswim) detached perspective.
But tell your dm to shut up (in the nicest way). They are brothers, even once he's been told, they're still brothers. Can't believe some people can be so tactless. And I think tactless is a nice way of putting it.