You state "....just too expensive for us to afford", then have a list of needs/wants. Why not include a relative budget figure so we can know what might be possible gear to solve your issue?
That said, yes. It might be possible for you to purchase a modest wired system with wireless speakers running elsewhere in the room. Depending on what sound quality you are after and how large the listening space is too, it may even be possible to get away with only utilizing wired speakers and skipping the wireless addition. Some of the Sony compact systems are decent in a pinch, like this one- http://www.amazon.com/Sony-CMTSBT100-Micro-System-Bluetooth/dp/B00DM5F19A/ref=pd_cp_e_3/191-5125756-3330844
If you wanted to go with your wireless idea, I suggest finding an AV receiver with bluetooth support, A/B speaker switching options. To add the wireless sound, pick up the rocketfish wireless unit from Best Buy ($79) or Amazon.
http://www.amazon.com/Rocketfish-Universal-Wireless-Speaker-RF-WHTIB/dp/B000VEP3XO
The rocketfish would allow you to pick up very simple but decent sounding traditional bookshelf/etc. speakers to use in a separate part of the listening room. Range is going to be < 100' between transmitter/receiver. And those speakers won't cost much if you walk into a used audio shop.
There may be other options depending on what the audio source(s) you intend on using is too (e.g. iPhone, iPod, tablets, etc.). Some newer AV receivers have apps to control everything too. Controlling an iTunes library w/ the Remote app has become a bit of a party standard. If you had a laptop with music library connected to a receiver, it would be really easy for multiple parties to be able to control the whole show if wifi was available too.
So, we are having a party and would like a reasonable sound system using bluetooth. This way, the person controlling the music can walk around and mingle with the guests while still controlling the playlist. Preferably the system would come with 2 or more un-wired satellite speakers so that we can place the speakers throughout the large living area . However, most of the speaker systems I have found are all wired or just too expensive for us to afford. Is it possible to buy a traditional wired system and add two single unit speakers and set them to run off the wired system? What would be the logistics for doing this?
I know nothing about audio set-ups but this must be a system we can easily remove, as we are renting the a house for the party. My last question is what kind of system (just in general) is a good one for this purpose? Am I going about this all wrong?

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