I'm so sorry for the situation you are in. It's hard, very hard to watch loved ones suffering and to know when to encourage them or when to hold them back.
I'm wondering also why you aren't allowed to enquire about her pain, has she asked you this, or have the doctors said so?
To the point of tears, well it depends on what type of tears, is it tears because she thinks no one believes her, tears because of pain, tears because she just doesn't want to go because she is a teenager, tears because you are making her? Like all of us in constant pain, we can be moved to tears because of a number of things. As a young person now, it would be very hard to not become resentful of you down the track if you force her to do something that causes her future problems or undermines her current health unless you have an open and frank discussion regarding the benefits she has to gain from social interaction and learning opportunities. It's important for her current and future mental health that she sees being out and learning as something good for her and not just something you insist on her doing.
With the home bound teacher, can you engage them in discussion about creating learning opportunities that are interactive and motivational for her? Is it about funding available to them? Can she be teamed up with another individual in the area for home schooling so there is more to it than just her being on the receiving end?
You are a wonderful and caring parent to reach and put yourself out there amongst us long term pain sufferers, we have all at some stage been exposed to uncaring or ignorant family members and the pain we experienced from those occasions often drives our thoughts in today's world.