How can I temporarily remedy the rotten, leaky roof on a mobile home?
Purchase a roll of reinforced (fiber-embedded) polyethylene sheeting of a size adequate to cover your entire roof. Also purchase enough 2x4 lumber to ring the entire roof, minus 10% or so. Procure a hammer or squeeze stapler and staples, 3" construction screws, and a good cordless drill and bit.

Roll the tarp out over the roof. Trim it so that the tarp extends past the roof about 18" on all sides. Staple the lumber to the edge of the tarp, then roll it in the tarp until the lumber is inside the edge of the roof. Screw through the tarp and lumber into framing below. 

Do this all the way around, leaving gaps of 6-10" between each board. Now cut drain holes in the gaps between the lumber along the eaves (as opposed to the "rakes", or the sloped roof edges). 

If you have penetrations (plumbing and furnace vents, for example), you'll need to find a way to waterproof them as well. You may be able to sandwich an open cap down on them to pinch the tarp, sealing it to the vent opening. 

Finally, lay sand bags or other stable, heavy materials on the tarp as needed to prevent billowing in the wind, which will eventually tear the tarp.