I feel as though you're getting a lot of ideas here and not much in the way of resources, but resources are a bit tricky without knowing more about what your DD needs. You could try Murderous Maths: The Phantom X, although she might find it a bit childish if she's not into its rather cartoonish humour. Or, going to the other extreme, you could consider getting her a university textbook on introductory algebra (as you may know, algebra really means something quite different at university level than at school level, but a possible approach is to go deeper to understand the school stuff - sometimes it's the school's "just don't worry about that dear" that actually makes things hard). I love Cohn's Algebra Volume 1 (and 2 :-); his Classic Algebra seems to be essentially the same book; neither seems to be readily available as new printings, but there are lots of second-hand copies around.
One thing that I think might be confusing about negative numbers, especially for someone inclined to think deeply, is that there are two really quite different things going on: the ordering ... -2 < -1 < 0 < 1 ... and the addition, i.e. that -n is
defined to be the thing which, when you add it to n, gives 0. You DD probably doesn't want to go quite as far as
Euclidean domains but you never know! At least, it might help to let her know that there is deep theory associated with this stuff: if anyone is telling her things should be obvious and she thinks they aren't, she may well be the one who is right.
