I think you should understand that there seem to be different rules around The Villages as to catering!
Once upon a time, the only caterer allowed was La Hacienda - a Developer-connected outfit.
Now, I believe that outside caterers are allowed, BUT there may be restrictions.
I advise that you discuss what you want with the folks at the Rec Center you want, to be sure that they can accommodate your catererer, as well as your booze provider!
Some of the rules allow the caterer to deliver to your chosen rec center, but your club memebrs must serve (and clean up). Then, I believe there are rules which allow you to hire a caterer who will do it all!
My bottom line is: If you want to have a party (private or not) at a Villages facility, sit down with a Villages representative and work out the details/ramifications! In the long run, I think you'll find a totally acceptable outfit!
SWR