Tile and grout like to be on something "solid". Now, don't get me wrong, the people I have loved the best lived in mobile homes, my grandparents, and I spent a lot of time in them. And, I am pretty sure that technology has not changed too much in the recent past. Therefore, I can safely tell you that your installation of tile in a mobile home will most certainly turn out to be a mess.
Lets look at this open minded. A mobile home has a minimal structure holding up a minimum of minimums. They put just enough into the units to get them into another county where they are parked. It is just not possible to put a quality tile job over the above scenerio.
Go to plan "B". Look for a "quality floor" that will take the abuse and is "flexible". There is nothing wrong with vinyl. It will just go down better and easier and last.....last........last.
Next you are going to tell me that you want glass blocks in the shower.