I'd say give it a go. When I bought my apartment building, it had the same issue, very dated linoleum. I could afford new carpet, but not new linoleum through out five units. So I did the vinyl squares and went to work myself. We ended up replacing them with linoleum over time when tenants would move out that was several years down the road. However they are much harder on what was much cheaper stuff than your Mom would ever be. Plus your Mom probably does things like clean her house too unlike some tenants.
Give it a shot. I'm sure it will work out well and the only argument might be how long it would last. My ultracheap vinyl solution still lasted about seven years so I'm sure this would last at least double that. The squares themselves never actually wore out. A couple of the tenants were just so dirty that dirt had gotten into the seems and over times created unsightly gaps. We replaced them for better visual appeal.
You can go into quite the Zen state when laying them down too. Bring some incense.