I have some questions for you.
How do you think your kids would react to being put in school? This must be a hard time for them. Even if you haven't told them about your illness, I am willing to bet they have picked up on something being wrong. If they would enjoy school that's great, but I know for my child if I were really sick and then I decided to send her away from me to school, that would be incredibly stressful for her. I would rather she learn nothing (which is impossible by the way!) and just be home with her family than to put her in school when I was sick. I just recently read some really inspirational emails about two families who had to deal with hard situations like this and decided to just drop the academics until it was over. One story was by a woman who wasn't even a homeschooler until she took her son out of school to accompany her with her sick dd to a hospital far away. After months of that and "no learning" they went home and they found he was ahead of his school class. Now they are homeschooling
Is this something that you will recover from or is it lifelong and you have to change your life for good? That would color my answer too.
Also, you do NOT have to drop everything the minute your child asks a question. Even if that were unschooling, it would only be possible for SAHPs of singletons, right? You can tell your children "that sounds interesting! Let's write it down and look it up later when I'm not so tired". My dd and I try to keep a log of questions she has. Sometimes we forget to research them of course
But often I'm in the middle of something or we're out on a walk and she asks me something I don't know, or whatever. So later we google it or ask her dad or go to the library or something.
I would still ask them to help out with things they *can* help out with but that's not my educational philosophy but my parenting philosophy
You say you can't do school, but how much are you talking about? Can you still talk to them just like a normal (non-homeschooling :LOL!) parent? And can you read to them every now and then? If the answers are yes then you can still homeschool. Throw away the curriculum, the workbooks and anything that your kids need served to them on a platter.
And absolute worst case, you *can* put them in school in the middle of the year if it's not working for you.
I hope you are recovered soon!