I do them at home and I have cream walls, splashback is minimal in the tent but I'm not sure I could say the same about one of the stands as they must splash off the back I imagine.
I've been doing this for 3 years and the only time I had a problem with mess was when I put the tube on the wrong part of the gun (I'm very clumsy!) and it squirted out and backfired at me and the wall and every single one of my products and equipment and stained all the lovely packaging. But it is easily cleaned up (just make sure you have gloves on!!)
As for cleaning up the tent, I have a towel inside it for when I'm spraying so there's no puddles left, and use a multipurpose cleaner on the windows followed by window cleaner as they can go a little brown after a few uses. The actual tent material cannot be cleaned successfully it just foams up and looks worse, I would advise against it. They only cost £40 and I've gone through 2, so would buy another one should it get really really dirty.
The floor..I have a wooden floor I would not do a tan in a room with carpet. To keep it clean I take off their sticky feet, wipe their foot with baby wipe and then put it on a clean towel and repeat with other foot. Ask them to do a wiggle and then when dry can walk around. As previously I used to wonder why I would get brown feet myself when I'm in 'home' mode and obviously it was residue.
With the cream walls it means I can use bleach without ruining the paintwork and if there's a splash I can wipe it away with a sponge and wahsing up liquid but that doesn't happen often. Tents are kept n bags but mine is very tough so cant fold away, so it leans against a wall which does get blotchy but its not visible and Ive just cleaned it for the first time as its never been bad before.
Definately convince your nan, its my most popular treatment