Panadero,
1) I'm sure Rainman, and most everyone else here, figured out what you meant by "El Rey" (note: all the smileys he included in his post). I think that most everyone here that speaks any spanish at all already understood about how the "de" & "el" contraction works. I believe he was just poking fun at the AFFECTED way you were referring to the place.
2) I wouldn't necessarily use these chicas as paradigms on how to speak proper spanish.
3) While SOME of the locals may be referring to the place as "El Rey" rather than the way it is more commonly referred to by virtually ALL the guests that stay there, that DOESN'T make "Del Rey" somehow incorrect. After all, that IS the name that appears on the building, website and all its marketing materials and so would seem AT LEAST equally valid.
4) Since you're talking to "most people on the board" here rather than to the chicas wouldn't it make more sense to use the term actually used by THEM? By your acknowledgment the "DR" is what "most people call it on the board".
5) If you're trying to shorten the name, when spoken "Del Rey" and "El Rey" are equally long (2 syllables). When written (as was done here) "DR" (or would that be "ER"?

) is even shorter than "El Rey", so why wouldn't you use that?
Personally, when communicating with other international mongers on-line, I prefer to use the abbreviations "HDR" or "HDR/BM" (or better yet just "BM" since few of us actually stay at the hotel). I'm ABSOLUTELY certain that NONE of the local chicas use any of those terms, but I'm NOT trying to communicate with THEM. I realize that not many mongers use "HDR" either, but I'm sure all of them can easily figure it out. The reason I prefer "HDR" to the slightly shorter and much more common "DR" is to distinguish it from the "DR" for Dominican Republic which also comes up fairly often on this and other mongering boards.