Help!

We moved into our home which has an existing aggregate floor in the family room, adjacent bathroom and laundry room. It looks as though it has NEVER been professionally cleaned. My daughter cut her lip on one of the steps that lead down into the family room. I forsee many more accidents in our future.
This surface is hard and unforgiving on little ones.
The bathroom is the worst of these rooms in regards to cleanliness. The aggregate is a porous surface and not easily cleaned. I have small boys who rarely have good aim, if you know what I mean, and the area surrounding the toilet is a nightmare. I would like to quickly slap down peel and stick tile without any hassel of laying down a sub-floor. My funds are limited and I don't want to hire anyone. Is it possible? I would also like to add tile in my laundry room. Cleaning lint off of the aggregate is another hassel I don't have time for. Will the surface of the aggregate show through? Will the tile stick? Please help...

Thanks for any advice!

 

The vinyl tile won't stick unless you skim coat the floor with a latex fortified portland patching compound like ARDEX SD-F (2 flat troweled skim coats)

Then sand the trowel ridges if there are any to make it as smooth as a babies bottom. Then use liquid flooring primer, so the tiles get good adhesion.