I don't see the issues you're describing as school/homeschool issues, so I don't see sending her to public school as solving these problems. They all sound like very normal age-appropriate challenges, so don't trip about your hs-ing plan.
It sounds like she's doing pretty good on the home learning front. You already have some really good suggestions on changing the dynamic that's creating the stress between the two of you.
I just wanted to add that I definitely would not have art materials out for free access that my 6yo dd could not clean up by herself. That's not to say that she always cleans up the art materials (I am looking right now at a stamp set that has been on the coffee table for well over 24hrs), but that I would go CRAZY if she could pull out at any time materials that she's incapable of cleaning up. And we are a very pro-art family. She does get to work in more "grown up" or professional media, but that is something that I pull out occasionally and we use together or with a little more oversight than the daily art materials.
So for your own peace of mind, if I were you, I would definitely switch to paint pens or other water-based stuff that she has (and can handle) the responsibility of putting away when done.
A system that works for us: dd has a plastic three-drawer storage dresser, just the small cheap kind. Top drawer is Drawing materials with markers, pencils, crayons, stamps, stickers, etc in their own smaller boxes, all stuff that is easy to get out and put back. I let her use Sharpies or brush and India ink, but those are in MY art stuff which she (pretty much) knows to ask for (and usually gets); 2nd drawer is Modeling with pipe cleaners, modeling clay, beeswax, etc. Same deal here. 3rd drawer is Painting and she has the cake things of watercolors, paint pens, some cheap water-based "craft" paint she was gifted, sponges and brushes and cups--all stuff that she is capable of easily wiping up herself--acrylics, oils, and tube watercolors are in "my" (or the "professional") art chest, and it's not like I won't share these with her, but they're not stuff she can just get out whenever she wants 'coz it's not as convenient for any of us, you know? Other art/craft (like fibers) are in baskets or other units around the house, but nothing is "free access" that she can't handle on her own.
Anyways, my point is I hope you get some ideas on setting it up for her to where she can "do it herself" and please, please, for your sanity, swap out the oils as once-in-a-while stuff so you're not putting more energy into her art than she is!
Perhaps think about doing some Montessori-style "presentations" on cleaning up the art materials that are always available and repeating the presentations until they are very natural to her. The cleaning up part is just as valuable a part of the process as the act of creating the art!
I hope you're getting some ideas on how to resolve the issues while continuing to homeschool!
