My mum remarries a lot, and this is her fourth husband. Or fifth. I'm not counting right now.
Her husband wants to move back to Minnesota, to be close to his family. My mum agrees with him, and they are house shopping. Moving everyone up to that cold hell hole.
Trouble is, I am a sophomore in High School, and if I move, my credits will very likely be screwed up. Plus, all of my family and friends are here in Texas. Everything I have ever /known/ is here. My entire life. Same for my sister. She is lucky to have her father still around, and my mother is ripping her away from that.
My friend's parents have talked about it, and are planning on asking my mom to sign over legal guardianship to them so that I can stay in the state, and graduate with my class and such. But unfortunately, I don't think my mom will allow me to stay, even if she found someone she thought capable to take care of me, which isn't asking much, as I can cook for myself, clean, and take care of a house pretty much on my own, except for the fact that I haven no job and can't pay for anything. I'm not close to any family on my dad's side (a fight with my uncle stopped that.) and my mom doesn't trust her family, so staying with a family member is out of the question.

So, what can I do here? How can I convince her to let me stay in the state? Fair warning, she is extremely stubborn, and I have never been able to reason with her for anything. Once she makes up her mind, it's usually non-negotiable. But I need to at least try with something this big.

If she values education strongly enough you could bring up the screwed credits.

If you feel strongly about it, I say go for it. Bring up the credits, if she argues, I know a girl who moved from Texas to Northern VA and had to repeat an entire year because they screwed up her credits. Prove to her over the next however long that you are responsible. Explain exactly why you want to stay without making it sound like it's her fault or getting her mad. If she gets mad it's all over.

I've tried bringing up the credits. I've tried mentioning that she's ripping my sister and I away from everything we've ever known and all of our family. It doesn't phase her. I'm completely lost on how I can stay, without running away or anything. Do you have anymore advice?

Try talking to a school guidance councilor or someone. I would hate to have all my credits messed up like that on your last year :/