Keys,
I would recommend a recurve instead of a longbow. For a given draw weight, a recurve is going to shoot faster than a longbow because it is more efficient. This will result in less arrow drop and flatter shooting, which generally enhances accuracy.
PSE makes a couple of youth recurves that are in your price range. I'm sure you can find them several places online, but one place is FS Archery, whom I have ordered from before:
http://www.fsdiscountarchery.com/bows.htmI would recommend getting a draw weight she can handle pretty well and then get some arrows that are spined for that weight. Shooting cheap unmatched walmart arrows is only going to increase your daughters frustration with poor accuracy that isn't her fault. Shooting a bow can be tough enough without extra problems.
If she still has problems, you might try getting her a mechanical release, and see if that takles care of the problem. Manual release is probably the toughest skill to master.
Good luck and good shooting!
Greg