You're not going to stop the dog, but you can try to get rid of the gophers. They make spikes that you put in the ground and emit ultrasounds that will encourage the gophers to go elsewhere and will not disturb the dog. Hopefully they will find your yard unpleasant enough and move out, but I don't think there is any quick fix.... We are on 10 acres and there are pocket mice, who also live underground. Our corgi has dug some holes you could fall into... My husband has to be real careful when he's on the riding mower, but it's too large an area for us to try to do anything about it. With 1 acre you have a better chance.
thanks for the reply ,Yah I'm willing to try anything at this point : )
No advice, I can't stop my corgi ' from chasing squirrels. I had a doberman obsessed with catching moles and the holes she dug were huge.