Fortunately a new element is probably less than $15. The first thing I would do is turn off the water to the trailer and open a hot side faucet to relieve system pressure. Then open the outside water heater panel and look for a name plate to see if you have a Suburban or Atwood. If no name plate look for the drain plug. Atwood uses a nylon plastic plug and Suburban uses a metal plug.
Next lift the little lever up on the Temperature Pressure Relief valve. If water comes out then your electric element (if it has one) will be fine. If no water then yes yo might have burned out the element. The water heater will work fine on propane alone. In face it will work better on propane alone than it will work on electric alone.
Next step is to locate the water heater bypass valves. You might have to look in a cabinet or under a bed. But the valves will usually be mounted close to the back of the heater. Verify that the valves are not in the winterizing position. Here's a link to the valve positions.
LinkOnce the valves are set correctly turn on the water again and open a hot faucet to let the air escape from the filling water heater. Now find the switch in the trailer and turn the heater on to gas and see if it lights.