I just wanted to say thanks again for helping me out with this one.
I'm pleased to report that calm has returned. DD has understood amazingly quickly about not bothering the dog and she responds when I tell her to stop if I see her approaching him.
She joins in with me when I'm stroking him, but it's led and guided by me.
It's not perfect yet, obviously. She still likes to try sitting in his bed occasionally whether he's in it or not. It was a game at first because I kept going to get her out, but she's pretty much got the message now.
So, like I said, thank you again for your comments and kindness after the initial onslaught! 