Big fat hugs, first of all. Because you sound like you need one.
I have a ten-year-old. My heart is breaking for yours. I don't know what s/he feels -- if s/he wants to spend time with her father or just does it because s/he's court ordered to? I know mine would, given the choice, not see him. Courts here don't care what kids want till they're 14.
You know what I do when I get to that place of almost desperation because AXH is still a big whopping millstone around my neck? I do the same thing I do when the kids are going through a phase of unbearably bratty behavior: I think "all I have to do is deal with RIGHT NOW."
Because to me at least, the problem is often that when I get that stressed and worn down, I tend to think "it will ALWAYS be this way. It will NEVER change. I will ALWAYS be dealing with this sh*t, and what kind of life is that???"
If there's one thing I've learned, it's that things change. Constantly. Sometimes for the better, sometimes for the worse. But they change.
I try not to bring religion in here, but this is sort of a story that I think can be appreciated regardless of faith... there's a passage in the Bible that says, "Your word is a lamp unto my feet" and I never understood that... until I read about how, in ancient times, when the Israelites would be traveling at night, they would have walking staffs that on the bottom had a small oil lamp. Because when you're walking a path, you don't need light at eye-height; you need it at foot-height. And it doesn't need to light up the path 50 feet in front of you: It only has to shine enough that you can see where to put your next step down.
I think of that sometimes when I panic about the future. That I don't need to see that far ahead. I only need to see where to put my next foot down.