i decided to put my son in kindergarten this fall for that very reason-- i was seriously debating homeschooling (i was homeschooled from 2nd grade-high school and it was a good experience) but i think he will learn better from another person. he resists my attempts to have him read, etc, and is very bright at math, much like your daughter.
i think that a teacher will have an entirely different relationship with him than i do and there will be no struggles because he will want to please her... so i don't worry about him resisting learning in school.
why not do school for a few months or one school year, and then re-evaluate the situation? then you and she will know what environment she learns best in because she has experienced both. also, after some time in school her resistance to you might change.
there is also the whole un-schooling movement, which you may be interested in. i don't know much about it, but i think the basic idea is that kids learn through play and exploration and life, not through workbooks and sitting at a desk. sounds like something she could thrive in.
i think, though, no matter what, that you shouldn't try to force her. if you keep her home, figure out how to work with her interests, create and find games and fun ways to learn, and don't compare her to her sisters-- let her be herself. if you send her to school, pay attention to what she struggles with and help her figure it out.
i have learned that if i just back off and let him do this thing, he learns naturally. he just resists the force. he wants to learn in his own way, with his own style. he is now reading, but only when he wants to. if i just let him do it when he's in the mood and praise him and encourage it, it works better than saying "read this now!!" and expecting it on command. it's something that he's learned unconciously-- almost by accident!! because any time i sit down and try to "teach" him he doesn't want to. but he reads signs at the grocery store, cereal boxes, car logos... and now he's absorbed enough of it that he will read a few words in a book to me sometimes.
a random thought-- my friend has a son who they just found out was dyslexic and then everything made sense--why he wasn't reading or writing well, etc. his brain thinks differently. so now he has learned special dyslexic rules that help him use his brain to read and write and he is so successful and happy in school. at her age, it's still totally normal to write letters backward, i'm not suggesting that she is, but if it doesn't straighten out it could be something to check into and would explain her frustration.