Looking to replace a small patch of carpeting in my mother's home. I really wish I'd taken a picture, but the floor needs to be durable because it catches all the snow/slush/mud that comes with the crap-tastic weather and her love for gardening. So we've ruled out carpeting. She also said hell no to linoleum when my sister suggested that.

The entire house is hardwood, except this tiny 4x4 sunken mudroom/hallway inside her side door. It's sort of an awkward space, typical of the Chicago bungalow. It's one step down from the kitchen, straight ahead is the garage, to the right is open to the basement stairs, and to the left is the side door. It has a very ratty looking piece of carpeting since she bought the place a few years ago. Understandably, no one will replace it for her because it's such a small job.

I was thinking of replacing it myself with tiles, but I'm not an expert tiler by any means, and I have NO IDEA what the floor looks like underneath it, so that makes me nervous. It's an old house, so I'm pretty confident the floor won't be even, and leveling a floor so close to the basement stairs might be outside of my skill set. I was thinking maybe vinyl planks to match her hardwoods, but I can't find any information on if they'd be prone to slipping inside their expansion gap area with so few of them installed.

Any thoughts?