Ummm.. hosed may be too strong a word but the information they gave you is not correct.
Pure (24Kt) gold is yellow. Alaskan "placer" gold nuggets are less than 24Kt but usually yellow.
According to my copy of Jeweler's Resource there are 2 common 18Kt white gold alloys. One is 75% gold and 25% palladium, the other 75% gold, 5% copper, 15% nickel and 5% zinc. These both look white. Neither alloy should need to be plated with white rhodium to appear white.
By any chance does your ring contain gold nuggets? Does it have gold nuggets "paved" over part of the ring? Gold nuggets ARE typically yellow. Even if they were soldered on a white gold ring, the nuggets themselves would be yellow.
You said you were told ONE of your rings was white gold so the other one must have been yellow gold originally?
It's hard to answer without having your rings in my hand to examine. I'd suggest you look in the yellow pages under jewelers and find a "goldsmith" or a "manufacturing jeweler", that is, a jeweler who actually makes jewelery, and show what you have and ask if what you really want could be made.