They eat anything green. She'd have to kill the lawn and all the vegetation.

I've read that if you bury the fence one foot deep they won't dig underneath it.

But I can't help. I had enough trouble keeping them out of my garden (electric fence finally did it, which is more than I can say for the deer). Totally gave up on all the Internet tips (ammonia, smoke, etc.) that didn't get their burrows out from under the porch and garage. Sprayed the workbench, garage doors and porch posts with Bitter Apple, which at least seems to keep them from chewing the wood and plastic down to nothing.

I think unless it's a mother and babies (which the babies would be out and about by now, if that's the case), they won't try to fight your dogs, but will just run away. I'd actually let the dogs have access, on the theory that the dogs will harass the groundhogs into leaving, better and more consistently than you could possibly do. That's what I've seen, anyway.