Conifer Help
 

Hi, My next door neighbour has conifers all the way along the boundary between our gardens and they have been moaning about my dog escaping into their garden last week. The conifers are approximately 6' high on obviously the branches grow outwards onto our garden, I don't mind them growing over the boundary but to stop the problem with the dogs I would like to put up a new 6' fence but would have to cut the conifers branches right back to the trunk otherwise I would be losing a large amount of what is already a small garden. Would cutting off the branches on one side cause the conifers to die? Any help would be greatly appreciated as I have tried using wire fencing so the conifers can grow throug but the dogs just pull and chew it until it is damaged!

Thankyou in anticipation.