Hi J.,
Depression is a tough nut to crack. Some of it is stress related, some of it is brain chemistry. Do not expect your husband to be able to solve it. When he is good for a day and then "not so", you have to remember that he is also trying to run around and pick up the pieces that you don't get done because you can't get out of bed, and can't get things done. If the meds aren't working for you, check in with your doctor.
I think it would be smart to send the boys to school. If you are having trouble just getting up, and your energy is at a low ebb, they are probably not getting the quality of education you wanted them to have when you decided to home school. At this point, their education is important. Send them to school and see how it goes. If that doesn't work, PA has an online home schooling program -- it's a charter school -- and that may be a good alternative.
When the boys go to school, force yourself to do something. Something with people - an exercise class, a crafting group, something that will give you some challenge, and some reward. I have been a FT employee and a FT mom, and frankly, I find staying home depressing. When I had a job, I accomplished things. When I stay home, the only things I notice are the things I don't get done (the LR picked, up, the floor washed, etc, the laundry folded) At work, you get to see yourself accomplish stuff, and you can go home feeling good (most days) that you DID something. I think getting out in this world and being able to interact in a positive way with other people would be a BIG asset. It might help give you a reason to get out of bed, especially when you really don't feel like it.
Putting the kids in school elsewhere is not a failure, by the way. I have a masters degree and I have had my kids in public schools all their lives. While I fuss at times about the school system, and assorted teachers over the years, and often I wish my kids were challenged more than they are, I also know that they are getting opportunities to be with other people their own ages, as well as to interact with other adults than our circle of friends, and those social opportunities will be good for their adult lives, when they have to go to work and interact with a broad variety of people.
Frankly, I have a friend whose husband is a college professor. They had issues with the school and she homeschooled for a year, decided it wasn't working, and now my daughter's friend is in a private school more to their liking.
You can be a successful mom whether you homeschool or not. Do not look at the decision based upon what you think it the "ideal world" choice. We don't live in an ideal world, much as we would like to. We do the best we have with the resources and strength we have for each day. The goals are to educate your kids, to get your depression resolved, and to have the family function as a loving and supportive unit. Public school, or a good private school, might be the best alternative right now. You can re-evaluate the decision over time. See your doctor to see if together you can get the medication levels worked out so you feel more functional. Find some things to involve yourself in that are productive and help you to feel good about yourself. Bring the joy of that home to your family, and share the stories that they bring home to you. I have a friend who got a job, working 2 - 3 hours a day in the elementary school lunchroom. she LOVES it, because now she has stories to bring home and share at the supper table, just like her husband and kids do. It's opened up a whole new world for her. (She was a SAHM) It also gives her vacations that match her kids' schedules.
Don't be afraid to grab for something a little bit better than the status quo. Deperession is hard to tackle, but not trying to resolve it is devastating. Your family needs its mom, and as the mom, you need to work at being as healthy as you can be. Your husband will probably help with the details to get the kids enrolled in school, and they can get tutoring from you or the school if they aren't at the same "spot" educationally as the rest of the class (it will probably be different subject by subject), and you can check in with the doctor for meds that work for you.
When you get life back on an even keel, you will feel SO much better.