I'm so sorry about this keisi. I agree that you've done all you can, and DB has no right to expect anymore. Like Smileless, I suspect your DB has some mental and emotional issues, especially since he has trouble getting along w/ your parents, also - not just you - and, in a sense, he own wife who has to cope by appeasing him (poor lady).
IMO, you need to let go of the idea of seeing him and his kids when you visit country D since he is not responding to you. Disappointing, I know, but a hard reality. Chances are, if he replied, he would just say hurtful things, and if he visited w/ you and yours, he would just create drama and spoil your child's birthday celebration, as well. Is it worth all that?
As for your parents, given their own issues w/ him, I'm not clear on whether they took his message to you seriously or just relayed it to you b/c they thought they "should." If I were you, I would let them know I've done all I can for DB but not get into detail. I would let them know (kindly) that it's between you and DB and that you don't intend to drag them in the middle. And, in fact, that you won't discuss it w/ them. And then change the subject
They may be a little upset b/c they are clearly used to a dynamic of family members sharing their issues w/ other family members (a dynamic common to many families, I think). But I think it would be beneficial for all if they saw that you weren't going to participate in that dynamic anymore They also may try to raise the topic more than once and DB may give them more messages to send along. But I would be firm in refusing to engage, reminding them each time that I had nothing further to say and changing the subject.
The letter might be a good idea, and I get why Smileless says to give a copy to your parents. However, this perpetuates the issue of having them in the middle, so IDK. ... hmmm... If you feel the need to write, then yes, I would give the parents a copy just so he can't lie to them about what you said. But I would let them know this is the last time I would include them in the issue and again, that I would not discuss it w/ them further. But I think DB knows all the effort you've put in and that you love him, etc. So I think I might just leave things alone until he decides to reach out (if he does). But that's just me...