I have been out of work and in school for three years. I get no UI money and very little on disability. In addition to grad school and homework, I clean the house everyweek, do dishes, lawnwork and more. That's along with looking for work and helping out with various relatives when I can.
Your mother is right, she should not have to carry the load on her own when another adult is living there. You can't cook? Now's the time to learn, and it's an important skill to have. Tell mom you don't feel comfortable cooking and ask for lessons, do other things around the house and show her what you are learning in your classes. ( If you dropped out of school what classes are you taking on line?)
I tell my mom every day what I did for a job search that day, where I applied, where I interviewed and I am teaching her computers.
And her alimony has nothing to do with you and you would be paying rent to her - with her own money. How would that help- if it were me it would make me angrier . Good Luck in your job search - and try going to the Employment Office, temp agencies and networking with people you know. There also might be some non-profits that could help you. Contact Catholic Charities for ideas,,,they won't try to push religion on you, but are a great clearing house for help