Two questions. Is it possible to connect Processing to the Arduino using the WiShield 2.0 and if not, how would I go about connecting TouchOSC to the WiShield. I have done research online, but have not found a concrete answer. This video shows a good example, but does not give out much information as to how it is done--->Arduino robot controlled using Iphone! - YouTube.
Can't help you with the connectivity to processing. A quick solution would be to use a standard Ethernet shield and connect a little pocket WiFi router to it, e.g. A TP- Link TL-Wr702n to it and run it either in AP or Client mode.
That way you can use the ArdOSC library to control your arduino from TouchOSC. I've done this exactly as described. No WiShield necessary and full compatibility with the arduino Ethernet library and the other libraries that are based on it ( like ArdOSC, Bounjour etc.).
If you run out of program space on the arduino you can use a Teensy++ with a Wiz812 WiFi module, which is what my project is using now. Cheaper than an UNO with Ethernet Shield and halve the size.
Can't help you with the connectivity to processing.
I can, here is how I did it:-
http://www.thebox.myzen.co.uk/Mac_Apps/Processing.html