The dog issue is a never ending problem in most rural areas.
I wont shoot dogs , for legal reasons and ethical. I had many dogs in my life and just couldnt kill one unless it was aggresive and threatened me
Believe me , I've had several hunts ruined because dogs running around , but most of the times they've been put in by dog hunters illegaly hunting a tract that they aint supposed to hunt.....I must say these are in the minority . Most dog clubs have been pretty good though.

Get the law involved.