Your 10 yr old might benefit from an internet program but 6 yrs old is too young IMO. You can also use software programs for homeschool. We use Switched on Schoolhouse for a couple of subjects with our oldest.
Is it possible for you to find another H/S family in your area that you would trust to watch your children for a good portion of the day or a few days a week? I know how tough it can be as I go to college right now part-time and I will be H/S 3 kids in the fall and I work from home. My husband also works from home running his own business. Things get hectic at times.
There is also the option of putting them in school just for a year or two until you get a steady schedule going on a job and are more secure.
I have put mine in school and taken them back out a couple of times. That's always a possibility and you can go back to H/S'ing at any time.
46-year-old single (divorced), self-employed working, home schooling, mommy to:
12 y-o (private school)
5 y-o (home schooled)