Hi Op, I have had similar issues with my daughter.
Couple of things I would say:
Firstly if your daughter is anxious about doing certain things (eg going to school) then it is very unlikely punishing her will mean she is more likely to do them,
If you think about an adult who has a fear or flying, then what is generally recommended is gradually getting used to it - so going to an airport first, then sitting in an aeroplane etc. there's whole courses run for people to help them get over it in a supportive environment where they are in control of how far they go in confronting the fear.
Taking away internet/phone et might make an anxious adult get on a plane if they are scared of flying (in the same way that sometimes people will do stuff they are scared of if the stakes are high enough) but it won't fix the anxiety long term.
She is anxious and stressed, as are many many teenagers post-covid.
Your highest priority for her seems to be that she keeps up her education. That's a good priority. She also seems to have that as a priority - school is making her anxious but she still wants to be educated as she's suggested home education,
That's a really good sign and some common ground there.
What I'd suggest you do is talk to her.
Say that you want to help her. Say that you can see that she is finding things difficult. Say that for you, you want to help her through this period and do whatever you can to help. Say that you cannot home school, but that you will support her in whatever else you can do so that she gets an education.
And then ask her what support you can give her.
She may have ideas, in which case listen to them.
She may not, in which case just repeat that you want to help as much as possible.
If you send her to her dad's the most likely outcome, if he tries to make her do stuff she is anxious about without offering support is that she will become increasingly anxious and it may spill over into either self harm or upset with her dad. That is unlikely to end well.