Dr have already said she needs to attend school before she can be referred to home school
That is not true. If a child can't attend school due to anxiety, they are entitled to free education from their area medical education team/hospital school (different areas have different names). This is set out clearly in the SEN Code of Practice 2014.
These services usually only offer the core subjects, i.e. Maths, English and Science, but they can offer more to children who are out of school for longer periods.
They can offer one to one tutoring at home or small group tutoring at specialised units. Part of their role is to support the re-intergration of the child into their own school. These units are run separately from the units where they cater for children who have been excluded from school for behavioural issues.
In our area, the community paediatrician or a consultant has to refer the child. Contact your local SENDIASS service and ask them how it works in your area. The school may not be keen for her to access this service as they have to pay for it so you may need to take what they say with a pinch of salt.
Has your DD been referred to CAMHS? It sounds like she needs some decent mental health support and possibly a neurodevelopmental assessment to see if there is any underlying condition that has been masked, e.g. Asperger's Syndrome. Waiting lists can be very long so you need to get a referral ASAP.
In the meantime, you need to make life pleasant and low demand for her. Do things with her that she enjoys and encourage communication. What that is depends on her likes and dislikes but it could be going for walks, doing craft activities, going clothes shopping, going out for a cake in a coffee shop, visiting a local historical attraction (this ticks the education box too).
Try to make sure that your relationship with her is very positive and supportive. She needs to feel safe to tell you absolutely anything and know you will believe her, support her and help find any solution she needs.
You are absolutely right not to try to manhandle her. That would be dangerous, be likely to cause her further distress, damage her relationship with you and realistically, she is way to big at the age of 11 for you to ever succeed if she really fights back. It is just a very bad idea.