In regards to the portion of the story about eliminating the "exotic" "invading" mountain goats in Grand Teton National Park, the past 25 years of goat management in Yellowstone is a good reference.
Goats started showing up in Yellowstone in the late 1980's. The Park declared mountain goats to be an unwelcome non-native, but the sanctity of animal life has usurped "Park Service policy [which] dictates that non-native species be eliminated".
A flashback to 1990 shows how little has changed on the debate about managing these "non-native" mountain goats in national parks:
http://books.google.com/books?id=w0... mountain goats native to yellowstone&f=false
I don't think the NPS will get approval to kill the goats that have made it to Grand Teton and they're not going to stop more from coming.
In regards to the part of the story about mountain goats threatening bighorn sheep, this reminds me of the debate about elk contributing to the decline of mule deer. Some studies will show conflict, while others will show that the two species get along fine. The conflict will be greatest when one or both species is trying to survive in marginal habitat with limited resources.
Instead of proposing to reduce one species to benefit another, I prefer to identify limiting resources and then protect and improve those resources. Pitting one species against another and trying to decide which deserves a bigger piece of the proverbial pie may be necessary, but it isn't as productive as making more pie.