if your claims manager wants specific information from your t and doc then she should write to or phone them personally requesting it so they are aware of what they need to give you, after all you are ill, you should not have to be the ping pong ball between her and your care team! if she is unprepared to do her job then you definitely have a case to complain to HR that she is unco-operative and obstructing your claim.
good to hear there is a little progress in your case, good luck xx