I think it would be hard to homeschool and work part-time IF one is a very structured, school-at-homer type.
We are very relaxed and eclectic. When our finances were stretched to the limit, I decided to find an evening job. I waited tables for about 2.5 years, 4 nights a week. I worked from 5- 5:30pm till closing. Dh worked regular Navy hours.... 7:30-4:30. The only times things got kind of tricky was when he was on-call. A couple of times, he just took the kids to the hospital with him. Other times, our neighbors would watch them for a couple of hours until he got home. Didn't happen frequently, though.
Now we're at a different duty station and dh isn't "on demand" as much. Where we were before, he carried a pager for 2.5 weeks out of every month. He's never on-call here because the hospital has a different system. Because of that, he's able to moonlight in the civilian community. He works on Wednesday evenings and Saturday mornings for about three hours apiece at a cardiologist's office, and makes more than I did working at that horrible restaurant!
I have a homeschooling friend whose husband is also in the Navy, and she works in the deli at a supermarket (evenings). I'm not sure what she does with her son when her dh is out to sea.... he just recently got transferred to a ship. And I have another homeschooling friend who is a single parent and she does medical transcription from home. Personally, I don't think I could work at home. I would be too distracted.