You're probably only getting half your circuits because you're missing a service leg. You said it is connected to a 20 amp breaker with 10/2. That really sounds like you're running 120V when it should be 240V.
Your 10/2 can handle a maximum of 30A. The bare minimum change you need to make is to take out the 20A breaker you're connected to and put in a 30A single pole breaker. You will get a voltage drop of around 5% with that length of 120. Pull out the 30A breaker in your sub panel and move the 15A breakers down one row. Only one bus is probably live in the panel right now. Put a 30A single pole breaker on the water heater circuit. (Skip another row in the sub panel for the same reason. ) ONLY DO THIS IF the heater can be set or wired for 120V. Your heater will heat much more slowly if you don't use 240V. This should be functional, but you will very likely trip your breaker if you're doing anything at all when the water heater comes on, depending on the actual current draw of the heater. The supply is definitely inadequate, and you will be relying on the circuit breaker to not let your house burn down. This is also 100% not to code.
If you can upgrade the wiring to the trailer, get a 50A two pole breaker, two 4 AWG conductors and a neutral, and run it through conduit. I will cost a few hundred dollars in materials, but it won't be a fire hazard.