I think your BIL is an arse, rude, inconsiderate and highly idiotic.
If he hadn't told you he didn't want you to do the newsletter, I'd have told you to tell him to shove it up his arse.
Can DH change jobs by any small miracle? cos personally I'd not speak to BIL again after an email like that, until he apologises. But I'm an ex depressive, and not one that lets go of grudges at all well...
I think BIL is one of those people who don't understand, nor know how to deal with depression... and he's belittling you as a result of this.
On some point, I think you DO have a right to want BIL to apologise to you for his rudeness, and not to want it all smoothed over. Perhaps you are being advised to let it drop just cos it's easier for everyone (you included) in the long run.
That it may be, under normal circumstances, but when you are struggling with mood issues and PND, nothing is that straightforward.
I have no idea what to say to you to help you out of this mess. I kind of do feel that there needed to be a little more concern for your feelings, and what you are going through at the moment, for DH to be a little more responsible for sharing child care and being there for you.
What to do, how to do it? not sure, but explain again and again how it is not appropriate, under any circumstances for DH to agree things with you and then just ignore his agreement and ditch his responsibilities.
That said, if you do agree to something with him and he IS sticking to his end of the bargain, then I'm sorry, but you have to go along with it, not interrupt what he has agreed to, and agreed in advance with you.
Again, tell him what you need from him, cooly, calmly and without getting emotional or upset or hysterical female... That'll only damage your cause.
Make agreements, BUT if he breaks them, wait till he gets back and then read the riot act, privately. Don't humiliate HIM before BIL and SIL, cos then he'll not be standing up for you in future.
I remember your previous posts and I wasn't as sympatheic before, and I'm sorry. This is a situation that is much worse than it appeared to be then, and one that is naturally bothering you and affecting you greatly.
Wishing you all the luck in the world, i really hope you sort this out.