I'm not sure what you're asking here.* Do you want trees and shrubs to block the path that the dogs take?* What alot of people do is mulch the path that the dogs take and plant in other areas.* If your dogs are running a fence line, then make a mulch path there and plant shrubs on the other side of the path so that the path is between the shrubs and the fence.
Without knowing where you live, your hardiness zone and the sun conditions it would be impossible to make plant recommendations.* You might find this helpful.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.