Have you tried throwing a couple handfuls of moth balls down in the hole? Worked with skunks when they burrowed under my grandfathers house when I was a kid.

Now that is some big assumptions you are posting about my lifestyle.
The kittens are not in the house; and neither is their stink box. That is the wife's project in the outbuilding.
I just direct her to all the places on the property which need some wildlife repellent. Does wonders for the grass though.

Slap Ya Mama seasoning. I put it around the perimeter of my camper. It keeps everything away.

I bought one of these traps. Make sure and get the scented version. I set it up Thursday night for the first time. Caught one Thursday night and one last night. It’s expensive but beats “hunting” all night. Awesome trap!

https://www.thearmadillotrap.com

Plan to try one.

Fixed income. Not in your budget.

Worked for skunk under my patio, but it was touch and go when it came out.

To be fair, he just said used kitty litter. He didn't say who has to use it.

Texican's post reminded me of an armadillo incident in my much younger days. I had one digging up my yard and we finally saw it when we came home one night. I had my wife pull the car in front of the porch so I could use the headlights and I chased it and got it pinned against the fence. I grabbed it by the tail and it started thrashing around and damn near dislocated my shoulder. I could hear my wife in the car yelling out the window "get him honey!". I lost my grip on his tail and he got away. I was cussing and I could hear my wife laughing her head off in the car. Great memory.

They're almost a necessity in the country. I have four inside and three that live full-time outside. They are great mousers and I have no issues with rodents anywhere. I don't need or want them in my truck or equipment. My wife does the boxes for the inside cats cause she knows I don't like it. You keep the boxes clean and there's zero smell. And I wouldn't call them filthy, my three dogs are the ones that smell! But I love them all.

As far as the little armour coats, I had some digging tunnels under my house by way of under the deck. There was no way to get to them so I let loose a few rounds of 12 gauge off the deck and haven't seen them since.

I have never been a cat fan - I'm dog fan of Retrievers and German Shepherds that I have had all of my life. My wife brought home an orphaned stray cat. I love my wife so I tolerated the cat because he hung out with her and stayed pretty well clear of me. Then he darn near tripped me in the dark - pouncing on a scorpion about two feet ahead of my bare feet. He whacked it over and over until he gad it flattened out and quite dead. After making sure that I saw it, he left.

That cat must be able to hear scorpions, because he comes ripping into a room and gets any scorpion that gets inside. That cat takes out scorpions and other bugs long before we know that they are around. He has a litter box in the basement that I never smell because my wife deals with it.

I like this cat. My dogs like this cat.

Had one here under the garage. I ran a water hose in the hole and turned on the water. Didn't take long. He came out and got lead poison. Problem solved.

Mine simply made new dens under my house. :