We had two crossbred bitches, Anatolian Karabash x Irish Wolfhound (the karabash is a sheep guardian pretty much like the Pyrenees), 2 yo.
One was superb as both a guardian and because she got on with the flock and didn't stray. Her sister was not superb - she fought viciously with our other dogs then escaped and attacked our neighbour's flock, requiring 3 ewes to be put down.
Our view, and that of the neighbour too, was that it would not be possible to change her liking for chasing and attacking sheep (she never attacked ours, but then she knew them individually). We could have sought to rehome her away from livestock but because of the fighting with the other dogs on top of the sheep worrying, we took the very difficult decision to have her euthanased. She seemed to be two different animals - the quiet and loving indoor dog, then a killer outdoors. We couldn't risk her being rehomed with children or other pets, so it was our responsibility to make the decision.
My feeling, in spite of having one of the sisters as a wonderful guardian dog until she died of natural causes, is that crossing a dog which has been bred for one purpose such as guarding sheep with another which is bred for something different - in your case herding sheep, in my case killing wolves - can lead to offspring which don't know which way to turn and end up having to be put down.