I saw this today as I was looking online, and I think it IS possible to both homeschool and have a clean house at the same time. It takes persistence and routines, but it is possible to do both of these. They are not mutually exclusive of one another.
If you have read my About Me page, you know that I have homeschooled for more than 14 years and have six children. I have used routines I learned from The FlyLady to help me have a clean home and homeschool, too. The key for me has been my perspective on how tasks are handled in my home. I do not look at it as doing chores, and I share this philosophy with my children. I use the team work approach with them, and together the house stays picked up and orderly. I don’t strive for perfect either. There is a balance between a picked up home and one that is treated like a museum.
If you are struggling with getting all of your homeschool plans and home keeping tasks accomplished daily, you should start off with the Baby Steps with The FlyLady and set some routines in place one step at a time. You can find The FlyLady on Facebook, too. I highly recommend her emails.