Hi - you don't say what stage she's at, so I'll try to cover all the options:

1. Frequency is one of the main keys
2. You say it hilly - do you have a flat area where she can practise or is she past that stage? If not, a flat area can get her concentrating on the basics without getting too hung up on the coaster brake (I'm somewhat biased against them but others swear by them, so you takes your pick). It also means that she can move on to practising with the coaster brake without worrying about losing control down your hills - baby steps.
3. If she needs her confidence boosting by a little helping hand from you, I've found that resting the fingertips only between her shoulderblades give sufficient help without pushing her in a slightly different direction from where she's steering.
4. We use counting as a distraction - get her to count the number of seconds (very roughly) or pedal strokes she can manage before having to stop. We find that they're so focused on trying to beat their last count they forget it's hard
5. As far as coaster brakes are concerned, they're really an excuse for not installing proper child-sized, efficient brakes and levers. People have probably got tired of me pushing Islabikes (now mail order from Portland). they're expensive but superbly designed and built with all component sizes relevant to the size of the bike/child. You can get good s/hand ones on Ebay etc. they're stil pricey, but that gives you an idea of how well they're liked.
Please feel free to come back with any other info or queries - there'll be bound to be someone who can answer them