I am designing a GUI using the wxPython toolkit, which means it's being written in python2. However, I want to use python3 for the actual application code. How would I go about calling my python3 code from the GUI?
Talk over a pipe or socket
Enable such python 3 features as you can from __future__ or use a library like six to write code which is compatible with both.
Don't do this. 

Finally, are you sure you can't use wxPython in Python 3? There's nothing in the online docs saying you can't.
Call python3 code from python2 code