OP, the problem is that their diet is so varied. To get rid of pests without poison, violence or relocation, you have to diminish the food source. Groundhogs will eat grass if there's no other option so you're hosed in that regard.
Call your county office. As THEM what you can do, since they somehow see trapping and relocating as "cruel".
Insert hippies in local government rant here.
Call your county office. As THEM what you can do, since they somehow see trapping and relocating as "cruel".

Insert hippies in local government rant here.