Busy working & homeschooling mom here:
I am a midwife. I'm often at a class, or a conference, or a workshop, or prenatal appointments, or a birth...
Thus, we have a babysitter that we employ for the days that I'm not home. I assign the kids' schoolwork, she sees that it gets done, and I do the homeschooling on the days that I'm home.
You can be busy and have your own interests and still homeschool. The catch being that you do actually have to plan work for your children.