Rhodium is very hard to solder. A lot of "white gold" jewelry is actually rhodium plated. If you look at the jewelry repair forums, what they all seem to say about, for example, re-sizing a rhodium plated ring, is to scrape off the rhodium, solder the base metal, polish, and re-plate.
Weller says it can be done, and recommends a highly active organic flux. But this doesn't make a lot of sense.
What you've got going for you with the rhodium plating is that it's very hard so it won't wear off, and the fact that rhodium just plain doesn't oxidize.
If the function of activated flux is to clean off oxidization, why use it on a metal that does not oxidize?
Other side of that coin - rhodium does not plate smoothly. Under a microscope, it will look very pitted, and the pits may go all the way to the metal underneith it. Cardas says that's silver.
For what it's worth, aside from being a big pain in the ass to solder, rhodium is about half as conductive as gold.
Gold does oxidize, but only very slightly, and the oxide doesn't stick to the metal - it just flakes off.
It does wear off, but it's easier to put a thick layer of gold on something than it is to put a thick layer of rhodium on it.
ANYway - my recommendation is this:
Flux it with the best flux you can easily get your hands on, get it really damn hot, and see if you can tin it with your finest 63/37 tin/lead eutetic solder.
Don't use a solder that doesn't have lead in it. You need something with wetting ability, and tin/silver doesn't have a lot of wetting ability.
Since your insulator is teflon, you can probably get the metal really, really, really hot before you start to damage anything. Once you've tinned it, it'll be easy going from there on out.
Failing that, look in the yellowpages for an auto body supply or auto paint supply store, and go get some 1000 grit wet/dry sandpaper. Take the layer of rhodium off it where you want to solder it, and then tin that.