I homeschooled my 5th grader for one year. We both loved it. He was having emotional concerns and the break from public school was just what he needed. However, I kept him is public school for gym and speech therapy. I don't think that is allowed anymore. It's all or nothing. But, with my son's emotional concerns he especially needed: routine, routine and more routine.
It's many years later, and he is doing great in college. I would homeschool again in a heartbeat. Be aware when you homeschool, each state requires special testing and there is some hassel with that. Also you may be able to find a homeschool group in your area. I had joined one. There I met helpful people. I taught music to my son and another child, while his mom helped with math. So there can be social contact for you children.
I loved being within a framework, choose lessons and activities which were in line with his learning styles. For example, he learned to be able to quote the preamble to the constitution, then we drove to the state capital where my son quoted it to a senator. My son was so proud of himself. You won't find an experience like that in a public school.
It reguires a lot of work on your part, but if your up to it, it's a great experience.
Something you may want to look into are the laws in each of the states you plan to travel into. Find a good base state. For instance when I homeschooled, Iowa didn't allow parents to homeschool unless they had a teacher's certificate.
Raising kids is a big job in itself, no matter what. When it comes down to it, the decision is yours I applaud you for asking questions. Keep asking.