Two days of 60-70 degree heat I don't think you have an ice problem. Do you have hot water anywhere in the coach and only not at the kitchen faucet?
Sit back for a minute and just take in the trailer. Think about the location of the water heater to the faucets. Most likely the trailer only has one water line that runs from the fresh tank, through the heater and then to all the fixtures.
Run run hot at the working faucets and then start tracing the water lines touching the outside of the lines until the temp goes from hot to warm. Hopefully you can open cabinets or pull out drawers to reach the lines. You checked the outside shower knobs, what about the inside shower?