I know it sounds brutal and inhumane but get a shock collar, crank it on high and knock Hazel on her butt everytime she chases a bird but allow her to be around them under your supervision like when you're gathering eggs, releasing and penning them up, etc. It doesn't take long for a smart dog to learn the rules if you are firm. You need to get her trained before she kills a bird, then it's too late and you'll never be able to trust her around birds again.