wow. this is a horrible situation.
the sad truth is that whatever reaction you would have had and whatever decision you make - one or more people are not going to be happy. another truth - your DB is an extremely selfish, thoughtless person who, even after you highlighted the issue this could cause, he made no attempt at remedy. I don't think he likes your 'new' wife. He has zero respect for your 'new' family.
there is no 'right or wrong' - in the way people are feeling or how they should feel and how you should react.
everyone's reactions are understandable and valid.
If I were:
your wife I'd interpret the invitations as a very clear (passive aggressive) message - your children don't belong in our family and are not seen as part of our family. I'd also think that they were inviting me, as your wife, only because they have to.
your DSC - I'd probably never really recover from the blatant message that, even though my step dad has been the most constant (as in daily upbringing - no comment on bio father here) father figure of my life and, notably, since an age that that's all I know as family (one of them was only 3!) - I've never been seen or accepted as my DSF's child by his family. I'd be extremely self conscious and feel vulnerable and exposed every time I had to see or interact with this family who do not see me as family. This would potentially cause issues for my family unit - especially my DSF
your (biological) children from your 1st marriage - I'd probably feel and react exactly as they have. You left us for a new woman. You chose to live with her rather than with us. You became a father to children you aren't even related to rather than stay with us. Those unrelated children see you every day, you live your life with them, you do things with them that you've never done with us. I was practically a baby when you left me. And now you're not coming to our uncle's wedding because he didn't invite the children you prefer to be with who you aren't even related to???!!! So you're still putting those unrelated children first - before me - your actual child. I may never recover from this. I think I hate you. And I firmly believe that you probably don't love me and if you do, it's only because you have to because you're my dad.
your ex-wife - I'd think wtf are you doing! why are you making your children feel less important than they already do. How dare you hurt them this way.
good luck mate.
FWIW, if I were put in that postion, I would have immediately called my brother. I would have explained that not inviting my DSC is not an option. I would have said that even though my having two families is not anything to do with him, it is a reality and his not inviting the DSC will have a massive negative effect on the whole family - including the actual DB. I'd explain that he doesn't even have to like them or accept them - you can't make him, it's his choice - however that's irrelevant as they must be invited so as not to cause unnecessary potentially irreperable damage to an already complicated family set up.
your DB has put you in a situation that has no positive outcome - very unfair. as I said, good luck.
Once the wedding, honeymoon and a few weeks have passed, you should sit your brother down and explain to him what his thoughtlessness has caused. It may also be a good idea to let the whole family know that your wife and her children are your family that you live with on a day to day basis and should be regarded that way.