There's no two ways about the physics. Heating water at a temperature rise and flow rate sufficient for a shower requires between 50 and 100 amps at 240v, depending on the temperature of the cold water.
For an all-electric trailer, you would therefore be best served by a tank-type water heater.
There are three options:
1) You could install an RV-type dual fuel (gas/electric) water heater, and just use the electric part of it. Atwood and Suburban both make them, in 6 and 10 gallon sizes.
2) You could install a small house-type electric water heater. 2.5 gallon and 10 gallon are the commonly available sizes; 2.5 gallon is probably too small. 10 gallon may not fit the space you have available. These are both available at home centers, and cost about the same as RV type water heaters. You can retrofit a heating element of differing voltage or wattage if necessary.
3) You can get a marine water heater. Propane water heaters are typically not used on boats, so the marine ones are electric only or electric plus heat exchanger. Again prices are about the same but you may find that the shapes and sizes are a better fit for your situation:
Marine Water Heaters