@Pleasehelpimexhausted It sounds like with a chronic illness in the mix plus two young children you really have a lot on your plate, and that strategies to help a bit with the overwhelm are hampered by being rural and not being able to drive. I really feel for you.
Ignore this if not helpful, but just trying to think outside the box: could you afford taxis to and from a play group or activity for every morning / other morning of the week, for perhaps a few weeks? I found getting out of the house helped me a lot when at my lowest. It gave the kids much needed stimulation, and gave me a change of environment. And I could look round d and see how battered some of the other mums felt that day / week too, and helped me have a glimpse that my struggle was not unique to me, which made it a bit easier.
Also - where you said I have no fucking idea how to keep them entertained for 11 hours - I totally get this, and I used to find it extremely hard to occupy them (for different reasons, mine are both autistic and attention span low and sensory seeking needs high). What I did was make a very basic visual timetable board (laminated a4 sheet with two lines of Velcro stuck lengthways across it), then took photographs of all the activities I could think of, and printed them on little tiles and laminated them. Then each morning I sat either the kids at breakfast and let them each choose some activities to do that day, and then I assembled them in an order on the timetable so we knew what was happening in what order. I tried to alternate physical things with sitting still things. Eg:
Breakfast
"Gym" time in the lounge (wheelbarrow walks, rolling on a yoga mat, bouncing on mini trampoline)
Play doh at the table
Doing cosmic kids yoga on the TV
Listening to an audiobook
Lunch
Etc
I would recommend that whatever your kids seem to like, to throw loads of it at them. If they like water, you can do a water activity each day:
Sit in bath in swimsuit and wash all the plastic toys.
Wash potatoes and carrots at the kitchen sink.
If you have a garden, bowl of soapy water and sponge to wash a toy car like a car wash etc.
Arming yourself with lots and lots of different activities can be really helpful, although that needs motivation to get it going, which I know is in short supply when you're battling with depression.
Well done for asking for help on here - asking for help is a sign of strength. You will get through this x