My question involves unemployment benefits for the state of: Washington

I'm going to try to be concise but it's going to be hard because this is a year and a half of what's being going on. Basically I am wondering two things. 1. If I quit because I have reason to believe I cannot correct these mistakes and I will be let go or fired can I claim unemployment? Can I give notice due to family and mental stress issues due to this job?

I took a job last January 2012 and from the first month I was already have trouble meeting the expectations of the job. The job was drastically different than what my boss described at my hire interview and it was clear I did not have the skillset for it. Since I had recently graduated from college and needed a job very badly I stayed, plus they said they would be giving some training. I watched as employee after employee quit. The coordinator was the cause of everyone quitting and she very quickly became my problem to. We immediately clashed but since I had never worked with someone I didn't like I figured it was a good learning experience and so I stayed. Bottom line is she is terrible and is causing me anxiety to the point I don't want to go in to work every morning. Here's why.

Month after month the coordinator would find something, usually a very LONG list of things I didn't bill right or didn't do this right or that right. I tried to correct it and move on. But the next month I'd still have some of last months mistakes. It seems like no matter what I do she always finds something wrong with my work. It seems like she purposely looks for it, nit picks and does whatever she can to come up with something. Every month is hell working with her and it gets worse every new month. This causes us to have to stay late on days for HOURS and she is mean and ugly towards me and causes me to have panic attacks and anxiety from all of this. To make it short, I went on vacation and came back to an upset boss who sat me down and told me point blank that she thought this job was not working for me, that it was not a good job fit. I have to be honest and say I felt relief right then and there. I was thinking she was going to fire or lay me off. She asked some questions and I explained that I didn't think it was working either, that I felt the coordinator and I clashed and it wasn't a good job fit and I couldn't perform my all of my duties. Instead of letting me go or firing me she thinks I need more training and said that if training didn't work she had to fill my position. She made it clear that if I didn't learn to perform the functions of my job I am having trouble with I would be let go.

Problem is I CAN"T perform the functions and she knows it. It's been a YEAR and 4 months of this going on, every single month. There is no way it's going to change and I will lose my job. That's not even getting into the mess with the coordinator which is another book full of drama.

Bottom line is I was able to print out all of the email going back from the first month to serve as a paper trail of my inability to perform the job duties, me trying to get it right and it not working out.

In a situation like this can I resign and still get unemployment benefits? I've been trying to find another job for a few weeks now but there is nothing in my area and we can't move. It won't be easy for me to find something and I cannot afford to not have unemployment benefits. I don't know what to do

I can get into the other issue with the coordinator and how that's effecting my mental health but I don't want to cause you all to read another huge post unless necessary.