I second what all the other posters said. When my AH and I were separated, I did my best to find back up care for when I absolutely needed to be at work and 1 of my kids was sick. I did not rely on AH because at the time, he was actively drinking and I never knew what I was going to get.
Maybe you are doing a great job at separation and your AH is now using your daughter's illness to get back into your life.
Do you have designated times when he cares for your daughter? If she is sick during those times then he will handle or get his own back up if needed.
I know I am making it sound simpler than it is, but it was always easier for me to not depend on my AH and let go the times it was his responsibility. Somehow he managed to not drink when he had to take care of the kids and if he did drink, well that was a different story and I didn't leave the kids with him.
Anyhow, you take care of yourself and if you are not comfortable, don't let your AH's response to your daughter being sick make you feel like you messed up. (((HUGS)))