I have been feeling like this lately, my children were just adding to my perma-stress headache.
It was a viscious circle. I was actually being very unreasonable.
I feel I broke the cycle yesterday by dancing around the kitchen with the children to ACDC, playing tag with them, cuddling them.... screwing everything else, stopping and being present. It was the LAST thing I wanted to do, but it was a tonic. I put on hold everything that wasn't related to them, the house is a mess, I haven't read the papers I need to for work, I didn't lovingly cook dinner, we had beans on toast.
I've been more productive today than I have been in a long time. I'm not out of the woods yet, I still feel exhausted and crappy, but I'm not taking it out on the children.
I have no one who will take the children overnight, no babysitter (can't actually afford to go out this month anyway) so I guess my choice was one of a) carry on in the negative cycle or b) refuse it. I've been on a walk this morning, a fast one, and sat on a rock for 1/2 an hour just thinking. That has also helped a lot.
Good luck with finding balance OP, you are not alone... x