Open Question: What can I do if 2 insurance companies each say the other is responsible to pay my claim so they both deny it?

I live in California, btw. So what happened is that I was taken off work due to extreme stress. There was no doubt that I really needed time off and was having a lot of physical and emotional symptoms due to the stress. It was mostly work-related, and I was taken off for almost three months. Even the man who interviewed me from the worker's comp insurance company agreed that the conditions under which I was working were horrendous. However, the worker's comp insurance company denied me, saying that more than 50% of my stress was due to factors outside of work. So then I went to my private disability insurance company, and they denied me saying that worker's comp was liable, not them. So I've been struggling financially because neither company wants to cover my loss of wages. I'm back at work and it's improved a little, so I'm catching up on bills. But still, I need that money back. What else can I do? I already appealed once to the private insurance company and they denied it again. Is there some third-party that can investigate and decide which company should cover the claim? Oh and I should mention that I don't pay into state disability because I am a teacher. So it's a private insurance company that I'm dealing with.