I don't know if you can convince her to send you to school; the best you can do is present your case with your reasons.
If you are having trouble remembering facts, that's really no different than most schooled kids. This is why teachers have to review parts of speech year after year, you expect it to be a brief review but the kids come in and look at you like they've never heard of a noun before. Ask them to name 5 US Presidents and you get blank stares. A study a couple of years ago showed that something like 1/3 of American high school students could not find America on a map. So school is no garauntee.
Talk to your mom. If she agrees with school and it works for you, great.
If not, you need to tell her that you both must consider different approaches because you do not feel you are getting the most out of the methods and materials she is using..
For example, get different books; rent educational DVDs on the topic; take field trips; do more in-depth independent research studies; get a tutor in the subject, etc.
Try focusing on understanding, not memorizing. Go to the library or search the internet, there are literally TONS of resources that will explain things and one is bound to make more sense to you... there are science books not written like text books, but humorous and aimed at kids. There are the "For Dummies" and "Idiot's Guide" book series that break just about every topic down.
There are inter-active websites, youtube instructional videos, even computer games, etc., that you can use.
When you don't get something, don't let it go or move on in the book. Tell your mom it's fuzzy; ask her if you could both look up different resources until it makes sense to you, or seek out help from someone who might be able to explain it.
Whether you work with your mom, or in a school, or on an online program or independent studies, the people who are successful are the ones who seek, not the ones who wait to be told. Take a more active role and interest in the things you want to learn and no matter where you are educated you will find it pays off.
your mom is stupid. homeschool is bullshit, a history teacher would explain history to you so you would learn it easier . reading history is like sleeping with open eyes.it is not your fault. push her hard to get you going to school, if she says no stop learning, refuse to learn,protest works.