Hi Sweetthing,
I've not been in this situation, but felt i had to say the following:
The children are missing each other and as parents its up to us to try to make their lives as happy and contented as we possibly can. Yes we make mistakes and sometimes things don't work out the way we would want them to, but if at all possible we should try to make the effect on the kids as little as we possibly can.
I think you are almost there in answering your own question about eating humble pie! If it were me, and i'm not you, i would have to do my best to enable them to continue to be brother and sister, even if it meant i had to suffer the indignity of being nice to my ex. It will be hard for you, i'm sure. The kids will thank you for enabling them to keep in contact eventually i'm sure.
I deal with lots of kids whose parents have split up and the one thing they all say is that they miss their siblings, even if they did fight like cat and dog at times. Many of them have gone out of their way to get in touch with younger siblings, without parents knowing at times.
Sometimes we have to agree to disagree, it's just life.
I do think the hardest thing for you will be get your ex to agree but hopefully as a mum she will see that it's for the kids NOT you and her.
Sorry if i've overstepped the mark answering this, but as i said , i have so many kids who have problems because of parents splitting that i will do anything i can to stop more kids being hurt.
(Couldn't fit all this on a postcard hun, sorry!!!)
Take care babe
Luv Lady x