K.W.
Wow. It does sound very difficult for you. I had a little taste of that when I was on bedrest during a couple of pregnancies, at one point for 6 weeks with a 20 month old. I had to rely on the help of friends a lot. Sometimes they would come in for the morning, until my daughter napped. One day a week I would go over to our pastor's home, my neighbor would drop me off on her way to work, along w/ my daughter, and I would rest on her couch and she would care for my daughter and I.
One thought. Even though you are in bed most of the day, it would still be important for your daughter to have a consistent schedule, with a variety of activities. Can you vary the TV watching w/ some other activities? We always do a room time w/ our kids somewhere after breakfast, for about an hour. You could do something similar, but in your room. You could tell her where she should be, on a certain area of the floor, or in a comfy chair, or even in bed w/ you, and it would be time for her to play quietly w/ a few toys or a few books. If you're just starting out, you would have to keep the expectations low, like 5 or 10 minutes. This would be a time where she can't visit w/ you, just play on her own. Maybe at the end of that you could do something interactive w/ her, briefly. Then you could direct her to the next activity, coloring, or something that is manipulative. It is very important that she be using her hands a lot at this age, things as simple as playing w/ blocks, Lego, or passing a ball from hand to hand. Then you could allow her to watch 1/2 to 1 hour of TV while you rest. And then direct her some other activity, even if it is just to get out some blocks and build, or to play in a slightly different area of the room or house.
I have a friend who is a kindergarten aid, and they are finding out that children who have watched too much TV or too many video games, where they don't use both hands, have trouble learning to read. Using both hands helps w/ the crossover in the brain, which is necessary for learning to read. There are exercises you can do to train the brain, and they can learn to read, but it makes it tougher.
I think having you direct her day, which maybe you are already doing, will give her more security and boundaries, than as you said, watching TV all day. Even if she is watching more than you would like (if you weren't sick), I think if you break it up, maybe plan around her favorite shows, and let her know that you are still caring for her, and giving her direction, she will thrive. Keep pouring on the love in whatever way you are able, and maintain consistent boundaries for her. These are her biggest needs right now.
If you are struggling w/ discipline issues, perhaps your husband can partner w/ you in the evenings to do discipline and training, and communicating that you are parenting in his absence during the day, so that you know you can count on her obedience even if you can't get up, or if he is not there. She just needs to know that you are in charge, even if you can't get up. This will give her tons of reassurance in this difficult situation, and it's what kids need in any situation. Otherwise she will feel a bit lost and as though it is up to her to care for herself. There is nothing wrong w/ her being a bit more independent than other kids her age, and helping to care for herself, as long as she knows this is your instruction to her, and not just a survival skill she has had to figure out on her own.
Is there a church or pastor w/ whom you can share your needs? You really need some increased support. Can your doctor give you any suggestions for some community resources? I know you probably hate to get anything state involved, but is there a Head Start program that she could get involved with? Or would you rather keep her home w/ you?
Blessings, and grace to you.