I'm not sure what you mean. The terms "primary source" and "secondary source" refer to texts used in research, not to paintings. You might use one or both types of texts for a research paper ON a painting.
If you are using to "Home, Sweet Home" as an illustration to support certain claims about the Civil War, you might be able to claim it as a primary source since Homer did have immediate experience of the War as a war artist. I might be willing to accept that claim from a student, except that you must remember that Homer, like all artists, altered and recreated scenes for aesthetic reasons: his paintings (and the illustrations he did for Harper's) were not photographs, and the paintings were created sometime after the initial drawings done at the front.
I think you need to discuss this with your instructor, whose views may be more rigid -- or even more flexible -- than mine.
