Right I am back, and would like to address a few points.
Someone asked how hard the dog has to be hit to scream? She'sa greyhound, she's a known screamer, the vet even laughs about the fact that she screams at the vets before she's had an innoculation. When she's going out for a walk if she stands on a stone or gets snagged by a bramble she screams.
The house is plenty big enough for a large dog and she gets walked for 90mins a day.
There is no violence or aggression in the house that DD is picking up on. 
Nor do I think that DD is going to grow up to be a delinquent or a serial killer. I am not allowing this behaviour at all. I am trying to sort it out. I do believe I can sort it out and this is what I'm trying to do. I'm not currently rehoming the dog because I believe this can be sorted, I love the dog and I'd be worried about where the dog may go. And yes you can all snigegr away and say she could go somewhere where she isn't hit. I know that but like I said I am going to sort this out and do believe she could end up somewhere worse than this. She's a member of the family and I'm suprised to be honest so many people are saying to rehome her so quickly when normally people here are slated for being so quick to rehome their dogs. When we got the dog she was nervous of people, had never lived in a house before. She is still nervous of strangers and will pull away on the lead when we're out to avoid people.
We've had her over 2 years and this has only been going on for about the last 4 months. The situation that I believed started it is a time when DD leaned over the dog to get to a plug socket behind the dog, dog was asleep and obviously started the dog who jumped up and snapped and caught DD on the end of the nose. Please note that DD had never hit the dog prior to this. She had been told about leaving the dog alone on her bed, etc but I think she just thought as she wasn't actually touching the dog that the dog would remain asleep. She learnt a big lesson that day and now won't go to the plug socket. I explained about how she should have come to me and I'd have spoken to the dog to let hte dog know I was there, etc before leaning over her.
Anyway the dog is normally very well behaved. She's been to training classes and has fantastic recall and she will go back to her bed and lie down when I tell her to most of the time. She would never lie down if DD tells her to and also the dog ignores me in a couple of situations. Mainly if the fridge is opened or if someone is walking across the room with a plate of food or in the morning when I'm getting DD ready for school. At these times she's like a cannon ball, charges across the house and flattens anything in her way. Its been at these times that DD has hit the dog, its still no excuse and its not a reason and I am not condoning it, just trying to set the scene. The dog is very food orientated and won't calm down in these situations. In hte morning when I'm getting DD's shoes/coat on for school the dog is going nuts, in a happy, excited way but again flattening anything in her way, barging past people and jumping up. I have to send DD halfway up the stairs to keep out the way while I put the dog's lead on and then tie the dog up for 5 minutes in the garden while I get DD ready. DD says that the dog scares her when she does this and I can only think that she's lashing out thinking that attack is the best form of defence. I've told DD that the dog isn't been agressive in these situations and I think she does know that but still finds it a bit scary and does get hurt by the dog (as I do) when she runs over your foot with her claws out and whips you round the face with her tail.
We did have a couple of sessions with a one on one personal trainer for the dog and she gave us some tips/advice but to be honest I thought it was nothing I wasn't already doing. It hasn't made any difference. I'm going to see in the New Year about a different trainer that someone has recommended and see if he will come over and try and help.