I haven't read any of your original threads about this so apologies if I'm missing something. I really don't get the issue and is mumsnet really suggesting the op moves her wedding for a clash with someone else's wedding who she doesn't even know???! Wow! Just wow!
There is a very simple solution, your sister in law goes to her best friend's wedding and your brother comes to yours with their children. If your sil is busy being bridesmaid she isn't going to want the kids with her anyway (although you mentioned an au pair so maybe they weren't going anyway?). Your brother could go to your wedding with the kids if he doesn't want to look after his own kids (that's another thread and a half) he could ask family to watch them or bring the au pair along.
I really don't get this not inviting other kids because they'll talk?? That made me laugh, I couldn't have given 2 shiny shits about family weddings as a child, there was a disco and cake that's about it, I didn't discuss my cousins/auntys wedding afterwards, it doesn't interest children!
Your sil sounds like a bit of a dick. If I was you I'd ignore her, invite my brother and kids and draw a line under it. If your brother decides not to go to your wedding well that's his choice, it's shit if he won't but you know where he stands. My sister in law (husbands sister) and partner had booked to go to Australia on holiday before we booked our wedding, We chose the date that worked best for us, she was away but that wasn't our problem. The sil decided to move her ticket and go out later, the partner flew out without her on the date booked so didn't come to the wedding. If s'il had decided not to move her holiday I wouldn't have cared, it was her choice.
You can't let something so ridiculous ruin your wedding. If people don't want to come to your wedding and feel they have more pressing engagements well they don't attend. It's unfortunate it's your brother but if you meant that much to him he'd be at your wedding, not his wife's friend's wedding.