I have heard of stuffing the hole with oleander leaves, pouring gasoline on it, and setting the leaves on fire. Then somehow blow the smoke into the hole with a hair drier. If you do that, practice first with paper, because oleander smoke is really bad for you - hence why this works.

When all else fails, a friend of mine made very small PVC pipe bombs with an electric detonator of some sort. The critter has to bump up into the charge to close the switch and set it off. I'm reluctant to get all the details from him. If I were doing that I would drag the battery wires out of the hole and hook the battery up after the charge was placed in the hole. Then if it goes off accidentally it is "safely" underground. He said he could hear the "whump" noise when his trap went off.

a little too atomic reactor for me.

Sure, you say that now...

You need to figure out what the 'varmint' is before you can effect any control :-) And if it is something like a raccoon, skunk or possum hunting for grubs or other insect larvae in the soil, there's not much of anything you can do. I even have squirrels that dig holes in the lawn to bury nuts but that's later in the year.

A 1-2" hole is not very big. How deep are they?

about a foot before they make a turn. I'm guessing voles, moles or tootsie rolls.

When using fire to burn out insects or rodents, make sure that you have identified all of the entrances. Many years ago I found an wasp nest in the ground where my young children played. I first poured about a quart of gasoline in it. I then thought about it for a while and the decided to burn it. Using a rolled up newspaper as a torch, I ignited the one hole that I was aware of. Immediately flames came out of several other holes around the yard.

I have often wonder if one of those had been near the house, how I would explain it to the insurance agent