Nice post, itzDirty. To more directly tackle the questions of if coyotes are invasive, I would argue no. Non-native on the other hand, yes possibly. If they weren't here all along its clear that they got here naturally on their own, "invasive" is usually used in reference to species introduced through direct human action. Further, even if they are non-native, they are largely filling a niche left vacant by the removal of wolves.
It's worth pointing out that the coyotes eastward spread was likely a direct response to the removal of wolves from the landscape. When you "shoot them all", there are often unintended consequences.
