As an adult with agoraphobia, I totally empathise with the whole 'not wanting to go out' thing. I understand that she's worried about the social side of home-schooling, but the answer isn't keeping her in school (where she also has difficulty in keeping friends and her anxieties are getting in the way of her academic learning).
I think that it might help to think about different types of socialising and how they make her feel. I certainly find some situations more difficult than others. For instance, going to a museum/science center/similar place with one or two other children might be quite good, because she could choose how much she interacted with the other children versus how much time she spent looking at the activity. Something open ended that she can drop in and out of (so doesn't feel trapped) might work better than something that she has to commit to spending the whole day/afternoon/evening at.
If she finds it really difficult to speak to other children, then starting off with an activity where interaction is limited might be a starting point - such as visiting the cinema/play/concert that kind of thing, where the focus isn't on her.
Depending on her anxieties, some kind of art/craft group could be good, because she can concentrate on what she's doing and drop in and out of conversations with those around her without seeming rude. This might not work for her depending on her specific anxieties, I sometimes get performance anxiety where I'd rather work on something alone, because I don't like to make mistakes in public.
But if doing things with other children is too much at the moment, then just try and find things that she's willing to do with you, without pressure. Going for a walk, visiting a petting farm, going to the beach, doing things shes interested in. Building up her confidence of leaving the house again gently, and maybe try and get some professional advice about graduated exposure if she is really resistant to going out for any reason, particuarly if it's something she'd normally enjoy.
The whole "don't understand her" thing, does sound like she's desperate for more intense friendships despite her fears. Maybe see if there are online (or offline) support groups for children with diabetes or mental health issues that would allow her to chat to other children who do understand.
Apologies if I'm missing the mark with this stuff, I may be projecting my own anxieties! Wishing her all the best, I know from experience that emotional and mental issues take time to sort out, I think homeschooling her so that she's not missing out educationally whilst she works on that stuff is a good idea. It means she can phase into social activities in a way that suits her at her own pace, rather than needing to face the scary immersive experience of going back into school full time and just trying to survive and cope with everything all at once.