This does not sound like a do it yourself job. Maybe I should just bite the bullet and have someone bust it up-since the old cast iron tub will have to be busted up to replace with a shower. I know how I felt when I tried to remove the wallpaper and found the walls ill prepared-then discovered that there were at least 2 different layers of wallpaper under the one I was trying to remove. Boy was I hot!!!. Wallpaper had to become part of my wall and get painted. That is probably how someone would feel about tile over tile.

I should have explained. The floor is typically more damp and cool than the surrounding air. Carpet prevents air circulation next to the cool damp surface and the carpet will also be cooler and damper than the surrounding air. Organic stuff collects in the carpet. Mold happens. Have you considered removing the vinyl and staining the concrete? You can make it LOOK warmer.

Thanks for your answers! glennsfc, Sorry I don't know the technical word for that. But with the word "peeling" ceramic, I meant the top coat of the ceramic tile is peeling off in a few spots on the tiles. There're not a lot of those but I just know they're there... I read on this blog that a lady installed vinyl tile on top of the existing ceramic tiles. I wonder if anyone has that experience? The ceramic tiles I have right now is not in extremely bad condition, just a few "peeling" spots, very light color and stained yucky stained grout. http://www.sasinteriors.net/2012/10/installing-groutable-vinyl-tile-lowes/ So I wonder if there's anyway to work this out... with a baby in the house, I don't really want to make a big mess. Plus I don't have a lot of time to do that... :( .

You new installation will only ever be as good as what is there now. If you are willing to take that chance, then following the above advice should be sufficient. Additionally, if you do not have an voids to fill, instead of patching you can use a liquid primer to facillitate a good bond if the existing tile is asbestos. It its not asbestos, you want to scarify (rough up) the surface with a heavy grit sandpaper to facillitate bond. If there is any wax coating on the existing tile, that wax should be stripped before scarification, patching, priming, or installing new tile.