Before you add homeschooling to your toolbox, I'm afraid you need to help your daughter address some very very serious psychological, behavioral, and learning disability issues. Although the school may have refused services in the 4th grade, more than 3 years have passed and you have a right to demand the school retest her. The level of services she is entitled to receive varies from state to state, but there is a minimal level of special educational services all children are entitled to which is mandated by FEDERAL law and it sounds like your child is functioning far below that threshold. She needs to be retested.
Think of it this way. In two years, your child is theoretically supposed to be capable of graduating high school, getting a job (or head off to college), managing a budget, moving into her own apartment (or dorm), and generally start supporting herself. Teaching these skills is supposed to be divided between parents and the schools. Once she turns 18, nobody (no government agency, private person, or charity) is going to help her. No employer is going to care that she can't perform her job because she's "anxious," they're just going to fire her. Landlords aren't going to let her live for free because she's too "anxious" to get a job and pay her rent. They'll just evict her. Supermarkets aren't going to give her food because she's too "anxious" to get a job. They'll just let her starve to death. Government will just wash their hands of her ... once she turns 18 she's on her own. Without dependent children, they won't even let her apply for welfare. Charities aren't going to expend their meager resources to help somebody who's young, able-bodied and healthy when they've got families with small children lining up for help. Your relatives will quickly tire of financially supporting an able-bodied relative too "anxious" to survive on her own and show her the door. If you and your husband get in a car crash and die tomorrow, are you confident you've prepared her to survive on her own?
Many schools are really sneaky about denying children services because SpEd costs a lot more money than mainstream ed. Schools are not obligated to inform parents about many of the services they have which children may be entitled to receive, you need to specifically request them, and even then you may need to fight to get them to provide them. Schools are also really recalcitrant about helping 16 year olds' as it's cheaper for them to just discourage her from going to school and quit and wash their hands of her. Therefore, before you go to the school, I strongly recommend you call your state Department of Education and find out who runs your schools Special Education Parent Advisory Council (PAC) or similar parent-run SpEd advocacy group. Every school is supposed to have one, though they differ in how active they are. PACs usually meet once per month during the school year and the parents who've successfully navigated the "system" help teach other parents the ins and outs of working with your school. You'll learn more from them about how sneaky your school is and what it takes to get them to help your daughter than the school will ever voluntarily tell you on their own.
Secondly, it's advisable that BEFORE you go to your school seeking special education services, that you have your daughter evaluated by her physician and referred/evaluated a second time by a PRIVATE specialist (such as a psychologist, psychiatrist, ADHD specialist, etc.). Get a letter from them stating they have evaluated your child and diagnosed them with "X" disorder, and stating what services they believe your child needs. Do this BEFORE the school evaluates her ... it puts them on notice you are serious about holding their feet to the fire and makes them slightly less likely to simply blow off your concerns.
Third, there are very specific procedures and timelines/deadlines you need to follow to the letter of the law in order to request these services. Your local Parent Advisory Council (PAC) and state Department of Education may be able to help you get a checklist of what procedures you need to follow to navigate services. If you miss a deadline or don't follow the correct procedure, the school can deny your daughter services, so it's critical you learn how to navigate the maze. Rule number one is to always get everything in writing. Rule number two is to always bring an advocate (often another PAC parent more familiar with the process) with you to all meetings. Rule number three is to meet all sneaky deadlines. Rule number four is to always be polite and reasonable with the school, but firmly let them know you know what your rights are and mean business (in other words, wag your tail, but don't be afraid to bare your teeth and growl if tail-wagging doesn't work).
Last, you've only got two years left of regular education before your kid gets shown the door and is no longer eligible for services (though if she's flunked grades you may be able to get an extension until she graduates). The school needs to do the primary job of getting your child caught up, so DO NOT offer to homeschool and let them foist off their legal responsibility to your child. Don't even let them know you've ever even CONSIDERED homeschooling or they'll try to pull a fast one and evade helping her. HOWEVER ... it's a good idea to secretly pick the brains of the homeschoolers and use whatever tools they recommend to help your daughter catch up. This job is too big for you to handle alone, but there's no reason why you can't use homeschooling techniques to make sure she doesn't backslide on weekends, holidays, and vacation periods and also to supplement any natural deficits in your schools curriculum.
Many states also have varying degrees of SpEd training programs and/or advocacy services available free of charge or at very low cost if the school is still being recalcitrant. I strongly recommend you find out what is available and educate yourself very quickly. There's not much time left before your child will be too old to get help and, after that, it will all come out of your own pocket. Good luck!
