It is easy to trap dogs. You use a fox set with a minimum 24" long stake or 2 stakes. Most of the dogs I caught in my fox sets just sat there. You should have a snare pole to release the nasty ones and someone to help. I never caught the same dog twice. Either the dogs never came back to that property or they never went near anything that smelled like fox urine again. The only problem I had was even the dogs that were nasty in the trap sometimes wanted to follow me home after I let them out of the trap.
In Pa. it is legal to shoot at dogs that are running deer, and in deep snow it is even encouraged. I feel the same way about snowmobilers but they have not changed the law yet. What you wrote sounds like dogs spooking deer, not chasing deer.