Your daughter needs to be scared straight.
Homeschooling her as a punishment isn't going to work. Of course she's not going to learn! She is strong-willed. You can force a child to do many things, but learning isn't one of them.
I think at 7-years old she does not UNDERSTAND the allergy. All she knows is that she has to sit at a different table. She does not understand the gravity of the situation. She needs to be thoroughly educated on her allergy.
When my SD was about 7, she went through a period where she would not wear her seat belt. Her mama would not make her wear one, so she didn't want to wear one in our car either. We tried everything, rewards, punishment, stopping the car, etc. She knew how to take the seat belt off, so she would click it off as soon as the car was moving. She thought it was FUNNY that we would have to pull over and wait for her to put it on (which she refused).
Finally we took her to a police station where she saw videos of what happens if you don't wear your seat belt. Some were kind of graphic for a 7-year old, but it WORKED!! She made the decision ON HER OWN, once she had the information, to wear her seat belt. She did not understand the gravity of the situation before, she only knew that she didn't want to wear it. She did not understand "accident" or "injury" or "death." She saw the slow-motion crash test dummy of the child in the back seat not wearing a seatbelt. She was crying when we left, but it made a lasting impact on her. She clicked her seatbelt on AS SOON AS SHE GOT IN THE CAR, and has never given us a problem since.
Your daughter needs to see a professional, like a doctor, and have her allergy explained to her in a way she understands. If you have to get graphic, get graphic. If you have to get scary, get scary. If you have to show her pictures and stories of kids who have died from peanut allergies, do it. There are lots of YouTube videos with stories like those. She needs to UNDERSTAND and BE SCARED.
In my opinion, this is the best service you can do for her. She will need to be careful her whole life, and you can't be there to protect her. My guess is she sees peanuts as something that is YOUR fault, something YOU won't let her have, and it's making her different.
My guess is she's in denial about it, and she's only 7-years old so she's doing it in an immature way (which is normal for her age). Even my almost 12-year old has a citrus allergy, and was in denial about it for a long time. She would say things like "you won't LET me have lemonade." Sometimes she'd drink it anyway, and then get a splitting migraine headache and she STILL wouldn't learn! Eventually it sunk in.
The choice to sit at a peanut-free table needs to come from her alone. It can't come from rewards or punishments.
Once she has accepted her allergy and understands it, then you can work on compromises. Can some friends sit with her? Can she be trusted to sit at a regular table and not touch any other kids' food?
My guess is she can't be trusted to sit at a regular table because she doesn't understand why in the first place.
I wish you luck!