Im so sorry this has happened to your daughter and you must have been beside yourself.
The graft does look so much better already
I had experience of skin graft on a dp, but this was 35 years ago and it was in an area that would be covered by clothing for most of the year - although a very large area and they took the skin from his thigh
you really have my empathy on dealing with this
one thing I would say is we just used a local solicitor who dealt with this type of case and didn't go through our house insurance. The solicitor put in to the insurance company of the other person separately - so my dp got his full compensation
originally when the paper work was sent of to establish how much the amount should be asked for from the insurance company - the amount cam back at say £15k, I then sent in a 2 sided piece taken from my diaries at the time. This doubled the amount asked for.
Id suggest keeping a diary, if you haven't already of every little thing that your daughter has had to go through.
I do remember that they took into account that my dp was already married and this reduced his claim for compensation, reason being he wouldn't have had to Showa new partner his scaring, also the fact he was male reduced his claim.
Hoping that any of this information may help you and your daughter