if you want to keep her in school, i agree with eepster et al. doctor for reflux, talk to the teacher and get into the classroom to see what it what.
but, if you are thinking of homeschooling, check out waldorf or unschooling at this age. it circumvents any power struggles about "learning" by focusing on what is natural at this age.
the focus in waldorf at this age is play, work around the home (you do it, they join in if they wish), cooking, handwork/crafting, songs and stories. being outside every day for at least two hours, more if you can do it, is also really important. gardening is valuable, if you can do it.
most of these things have a lot to learn in them--just because it's not 'academic' doesn't mean it's not learning. and, it's practical. cooking is math; gardening is science; crafting is art, math, science, etc (depending upon the craft!). so, there is a lot going on.
so if the solution is to draw her out of school, take a deep breath, relax, and enjoy. create a rhythm, introduce some things in a gentle way, and then go from there. in a couple of years, she might be ready for a classroom setting again.