I can understand why it is tempting to have control over the events of your child throughout his or her school day, but one cannot have that kind of control as a parent, and still carry on with their own life in order to remain and become stronger for the child as this child grows older, and acquires the challenges of adulthood.
If you want to be a good parent, let the child interact and develop in the school system. I understand the problems with the public school system, but parenting doesn't have to mean total control of your child, it means the ability to help the child sort out the accumulated false, negative, and occasionally ill-intended inputs from the "outside world" while you as a parent cannot be there to protect them. The connection developed between you and the child, where the child comes home from the outside world with questions and concerns is trust building and your interaction in this child's life during these years as someone the child can escape the outside world to are crucial.
In this opinion, I realize that I have some embedded assumptions about the level of interaction with the public you are willing to provide to you child. However, when a single person is trying to replace an institution (such as school) in a child's life, there is an inevitable sharing and rendering of time that the parent is giving up. The parent is a person too and must continue to strengthen and develop away from the child to some extent. If you want the child to go to college and continue schooling past high school, you are going to want to be a fresh perspective for this person to compare his or her worldview to.
For homeschooling to be effective I think you have to do sort of a checklist of strengths and weaknesses ie... Is the child a self motivator and have self-discipline? Is the parent self-disciplined? Is the child open to the idea? Does the parent have a good grasp of general knowledge? Are both able to stick to a routine where work is done, and takes priority? Can consistency be maintained? Homeschooling can be very beneficial if done correctly and consistantly. You have to decide if you are up to it and not let the child "slide" on work and assignments. If you can put together a structured learning routine, there is no reason you can't make it work. It is a big commitment not to be taken lightly.
Public schools should always be the last choice. If they won't homeschool, then they should send you to a private school. Your education is more important than any inconvenience of homeschooling. Also, many programs make it possible to help the child self-teach so the parent doesn't have to stand over the child all the time. You can join homeschooling co-ops where parents take turns teaching certain subjects. There are many options. If it is the choice of the child to stay home and learn, then parents should help in any way possible.
That would take some hard convincing. I would just talk to her about it and find a very good reason why. She would probaly need a pretty convincful reason. good luck.
You could look up co-op homeschooling groups in your area and offer your mom some solutions. Tell her she doesn't have to teach you all by herself. She can sign you up for co-ops where other parents take turns teaching subjects they are good at. Homeschoolers have groups, support groups on the internet (just do a yahoo groups search) and many resources. Homeschoolers are not alone and it is easier than ever nowadays. Also, your mom can be sure you are learning what you are suppose to learn. Public education is getting worse and colleges are getting pickier with their students. If she won't homeschool, ask for a private school instead. With the money she saves on school clothes and supplies, she can easily buy books on Ebay for your grade level or use Craigslist.org to buy locally.
I don't know if you could convince him to allow you to be homeschooled. Firt of all do your parents have the time, money, engery and resources to home school you? If so then he should allow you to be home schooled. Also, if you are already in school and being made fun of everyday like I was, I would for sure take my child out of school and home school them. They made fun of me from grade kindergarden to the 12 grade, always telling me how ugly I was. If that is your situation then he should allow you to be home schooled. Good luck:)
Compile information both pro and con on the issues.
Then choose a time when the involved parties are able to engage in a meaningful discussion.
Hint: Not in the morning household rush or the home from work time frame.