I am having difficulty figuring out an effective way to connect the two antenna together and allowing them to pass the Bluetooth signals back and forth. There seems to be many methods, and I am not the most knowledgeable with RF antennas and such. I thought that perhaps an enlightened individual could give me a push in the right direction so I am not going about a random "witch-hunt" for a solution.
First, to test feasibility, simply connect the inside and outside antennas together, using something such as a pair of panel-mount coaxial connectors installed in the faraday cage - or better, a coupling barel inserted through the wall. This should cost little in time and money to validate.
Next, select components for a diode-bias RF switching scheme workable at 2.4 GHz, and install this between the antennas, so that by changing the DC bias voltage you can electrically connect or disconnect the antennas.
Optionally, add a filter to pass only the frequencies of interest.
There will of course be loss is such a setup, but by keeping the overall distances short it should be workable. Applying gain would be very difficult, as in practical terms you would need to figure out which device was transmitting and enable only that amplifier, which requires a realtime understanding of the protocol.
If you device is battery powered and you don't need high speed, this sounds like a Bluetooth application. If you use Bluetooth Low Energy (BLE) the drawbacks are shorter range (50-100m vs. 200m) and that Bluetooth 4.0 BLE isn't backward compatible.
A good comparison can be seen here:
Comparison of BLE and WiFi-Direct
Also there are dual chip containing BLE and classical bluetooth:
See this post for dual chip
The future is hard to predict by looking at the past :P
Best Answer
Bluetooth and wifi serve very different purposes.
Bluetooth is designed for connecting peripherals to computers at short range (<10M) and moderate data rates. It aims to minimize power consumption. Think of it as wireless USB.
Wifi is designed for connecting computers to networks at moderate range (5-50M) and high data rates. It aims to maximize range and data throughput, while not being unduly power intensive for computers. Think of it as wireless ethernet.