Extermination?

Is it right or wrong to exterminate varmints to protect your own interests? What do you do with the coyote in the chicken coup, the termites in your walls, the mole in the yard, the moths in your closet, the mice in the attic, the roaches under the sink? Extermination? Try to co-habitate with them? Shoo them away?
What about a varmit that claims jurisdiction over all of the land, property, possessions, and person…control over the animals, plants, even seeds…uprooting your crops and robbing you of your sacred herbs and sacraments, setting fire to fields and forests? What if they had taken over to the point where they left you homeless and penniless fleeing into the hills to escape them and they follow you into the hills continuing to impose their will on you?