I'll be frank and say that twelve is the age I am least looking forward to. I will survive and it and lie low. I think that you have a higher opinion of your kids than I do. I consider my children to be quite limited in the scope of things they understand. They have their own opinions, of course, but their opinions are based on such a small range of information and impulses that I frequently need to just ignore them. I don't ban all processed foods and sugar. I'm a fan of moderation. I think we live in the world we live in and I'm not going to make my kids freaks. That said they frequently give people lectures about how terrible and bad the McDonald's we are eating is. *ahem* (It's not even once a month. I can live with that much evil. Sometimes it is the lesser evil.)
My point is that your daughter clearly wants to be learning more information. That means you need to impose the schedule and teach her discipline. She's not going to pull it out of whole cloth. Some people can. I did. Aristotle did. But it's not all that common. Most people need to be taught the routine of learning. They have to be kind of guided through the habit of learning. I'm not saying beat them over the head with workbooks or anything such as that. We do SSR (sustained silent reading) in our house. We all sit down in the living room with our separate books and read silently. (Ok, the kids are looking at pictures. So what. It's about building habit.) My husband loves to read aloud. He has spent his entire life waiting until he got to be a dad and have a captive audience. Every day he reads to the kids for an hour. They read some weird shit. Have you ever heard of Girl Genius? The whole comic series is available online, though we have the paper versions. They are pretty.
Not to be silly, but you don't have to force feed the classics to get your kid reading. But you may have to require that she spend the hours and hours and hours necessary to get good at it. Ask her this: do you want to spend the hours now when you don't have anything better to do (come on--you're 12) or do you want to be doing them while you are an adult trying to manage a job so that you also have to deal with shame for not being competent. This is a skill that only comes through practice. Sit your butt down and read.
But I'm really ok on every level with being bossy like this. It's my job to be bossy like this. :)
However! Of course you are free to ignore me and tell me where to stick it. I'm not your boss. :)