I home schooled my daughter her 10 years (she got her GED 6 yrs ago)...people's views were pretty positive because it is well known that good parents home school for the right reasons.
I do not know enough about your situation, but if you stay positive, upbeat and sound competent and responsible, it may just make you look like you are making progress.
Maybe choosing an online course, or buying the books is showing them that you have a plan would be helpful. Just be confident. You are raising your children, you are teaching them everyday and taking a positive step in the right direction of your kids education.

Have a backup plan in case it gets to be a bit overwhelming. Of course some days will be, but I found it much more fun and less work than getting up early and getting her off to school.
Also, it is not a 6 hr day like in school in case you are being told that. I spent a couple of hours and then let her do her homework. In schools it is that long because they have 30 other kids all moving at a different pace.
Let me know if that helps or if you have any more questions. I'm sorry I couldn't be of more help.