I have refinished a shower, sink, vanity and toilet in a 1972 Tradewind with very good results. I used a two part primer and two part epoxy finish from Midwest Chemical. They really aren't a do it yourself shop but if you have an HVLP sprayer and a freash air respirator you can have them ship small quanities. I checked out the website for refinishing on line and their stuff looks like it would be similar and easier to use. The price looks good, too.
Be very careful to follow the directions and also be very careful about avoiding the fumes. This stuff can be very toxic. If done well the plastic part of the bathroom will look like new and will be durable. If the metal drains are corroded, try cleaning them with an acidic clearer like CLR or some other bathroom cleaner designed to remove rust and minerals. Let it soak for a while then scrub it with a scotch brite pad. I was very happy with my results. It change the bathroom from disgusting to new looking. I don't have this trailer anymore but may have an old picture or two if you are intersted.