Two months is an insanely short timescale for such an ambitious project. Remember that image recognition is pretty damn hard, and the fact that webcams deliver relatively poor image quality doesn't make it any easier.
Given the timescale, I recommend you do everything you can to save time (in a sensible way):
- Find libraries for everything non-specific. You don't want to code webcam image capturing yourself, you don't want to dig into low-level code to inject mouse movement events, and you certainly don't want to deal with pixel formats and image data management yourself. There are libraries for each of these; find them, and use them.
- Two months is way too short to accommodate learning a new programming language on top of finishing the project. Use a language in which you are all proficient.
- Forget cross-platform things, forget shiny GUIs, as you don't have time for these right now. Focus on the core mechanism - face recognition. Get the core functionality right, that is, a really simply UI (a blank window with one button maybe, or just a command-line program), save the UI for later.
...C# would be a good candidate because it can easily integrate with C libraries (and C is still your best bet for the support libraries), and because whipping up a "works for now" GUI is a matter of minutes with Visual Studio; but if you have no prior experience with it, you won't make it in two months - P/Invoke (the technology you use to call C library functions) is excellent, but it takes a while to wrap your head around it; I wouldn't recommend using it without mastering the basics of both C# and C
...Java, as you say, makes it hard to integrate C libraries, but if you're lucky enough to find suitable Java libraries for what you need, I'd consider it the best candidate, considering it is your strongest language
...Python could also work out well; it has a rich set of libraries out-of-the-box, and wrapping C libraries for use in Python is fairly straightforward.
I suggest you split up the work for the first week: assign one or two programmers to each candidate language, and have each one find libraries and write a prototype that does the following:
- grab image data from the webcam
- do a rudimentary operation on the image, e.g. find the darkest pixel in the image
- move the mouse to a specified position on the screen
This should be doable in a week in any of the given languages; evaluate all candidates and go with the one that looks most promising.
From there, you need to fill in the blanks: write a core routine that does the actual image processing and translates image data into mouse movements. Either of these languages should be equally suitable, provided that you have the above framework up and running.