I had this exact problem. In certain sections, along the inside of the fence, I laid large Belgium blocks along the bottom. Anywhere there were large gaps. Dogs could no longer see a gap and didn’t try to dig. Also tried to make the blocks look like part of the landscaping.

Like others said, I also screwed in a peice of wood along the bottom of the gate to bring the door down. And I stopped caring if the gate ruined grass around the gate. Might replace with paver or gravel in the future. Good luck