Your trailer, like mine, is 38 years old. The fact that you get some reception to me says that is has a connection to the roof antenna.
But the fact that you have poor FM to me means that somewhere there is a bad connection. A cold solder joint, a broken or cracked wire, a poor ground, there are lots of things that could go wrong.
So, what to do? Well, you could look into the beige plastic box nearest your radio that has a 12-volt connection in it. If this is the one that has a sub-connection to your radio, have a very close look at all the connections inside.
When I had one of those connector boxes open on my '74 Sov, I noticed that inside there were a few capacitors, a choke, and a couple of resistors. If any of the caps have dried out, or if a resistor of two have aged poorly and gone to ground, you just replace them.
- Do as the original poster did in post #2, and just put in a new antenna.
- Rewire the roof antenna from the antenna to your radio.
Personally I would go with number 1 above; it's likely to be a lot less work. The Service Manual tell where to cut and how to hide the cuts, but to re-do the wiring from the roof to the radio means opening up the central interior ceiling panel, and to me, that sounds a bit scary.