Heck of a paragraph you wrote there, but as I read through it, I found that I could relate to you. Very close to my mum but sometimes she gets a tad too much. One thing for sure, start asking her how her day was, listen to her and ask if you could help her with something, for example when she cooks or clean the house Staying calm when your mum bursts into fury isn't wrong at all.
Her fault right there, so explain to her how you are, I did it with my mum and she completely understood. As for her comparing you to your older brother, that is just wrong, but I can see why she does it. She just wants the best for you, but if it bugs you, tell her how you feel about it and that you don't mean to hurt her feelings.
Three main things to keep in mind to keep a good relationship: trust, honesty and compassion. I hope this helps a bit. I've had the same story with three of my friends and I gave them the exact same advice and it worked.
If not,write out the pros and cons of homeschooling and present it to your mother.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.