That's a good question. My friend had several Large-ish tanks in the living room of a moble home he rented, and bought a 150 from some people that had it in an older manufactured home .
My guess would be that it would be fine, but I would also put some supports under the floor just to be safe. They may not be needed, but better safe than sorry.
I would think it would be fine, but it could depend on the age, condition and actual placement of the tank. One of the guys at my local LFS has a large tank (a little over 300 if i remember right) in a twenty plus year old trailer and hasn't had any problems. The tank has been set up for at least the five years I've known him. His tank runs lengthwise the same direction as the house trailer, so it's spanning several floor joists. I would be more leary if it were going the other way and only supported by two.
It really depends on the trailer and it's construction. We lived in a trailer for a while that had large I beams running the length of the trailer. I imagine that a very large tank could be placed directly on top of one of the I beams, that might put the tank in the middle of the room though. You might want to look at the condition of the jacks supporting the home, I know the trailer we lived in had several jacks that had settled and were no longer touching the structure of the home.
In some ways there's actually an advantage to the trailer home if setting up a large aquarium. It's real easy to access and build supports underneath.
Take a few rough measurements inside as to where you would like to place the tank, jump underneath the trailer loaded with this information and fiqure out where the aquarium will set as if you were laying underneath the tank looking up.......Which you will be.
Have a good look around and see if you would be comfortable with the support the area provides. If you have doubts and aren't sure which way to go you might ask your parents either to hire somebody or get a friend in the trades to take a look and make recommendations.