As far as I can see, everyone so far has followed you in assuming that your daughter is the problem, and not the school.
Easter school holidays are coming up (I guess). Have you got some time off work (if you work)?
Could you do some chilling out with your daughter? Get her really relaxed. Help her to forget school, forget all those things she's no good at.
Then, try and work some of that abstract 'learning' stuff into everyday life. Sing along to some of her favourite songs together. See if she can beat you at remembering the words. Get her to help you put a shopping list together, once you're in the shop, she has the list and tells you what to get.
Go out somewhere amazing she's never been, or to see a film she wants to see. At bedtime, hold her, ask her if she had a nice time, see how much she can tell you about her day.
In other words...
Before writing your daughter off as 'broken', and before trying to get someone to 'fix' her, please try to work out yourself just how bad it really is. Trust yourself to know your child well enough to be able to work out exactly what the problem is. Only then go find an appropriate specialist to help you with the problem. Don't trust a specialist to tell you if there is a problem in the first place.
All the symptoms you describe in your question could just be down to her hating school.