<< lay down new vinyl tile rather than ceramic. Is there a decent web-site
that shows how to do this? >>
Not worth the trouble. Instructions are on the side of the tile boxes. More
detail in any DIY book. Check at your library, box store, look in old issues of
"This Old House".
<< paste along with the non-sticking tile will produce better
Not likely. Just use stick on tiles.
<< Home depot rents out an electric tile remover for $48 per day. >>
You can use a heat gun if you have one or any common hair dryer. You still need
a scraper, putty knife, and stuff like that. And time, lots of time.
When you have the old tile off, the substrate will probably be a major mess. It
is hard to predict what you will find and thus impossible to suggest best means
of getting a smooth surface. Sometimes sanding will work, others will nail down
a layer of thin luan plywood. Don't attempt to be a hero, if you are
overmatched, call a pro and get it done in time for the holidays. That will
convince her that you have excellent judgement.