I'd like to use Processing as graphics engine but make it work inside a wxWidgets or Qt GUI application. Is this possible and are there any references?
Since Processing is built on Java, you can use the following Qt-Java binding for your project. http://sourceforge.net/projects/qtjava/
I am not sure how up to date that package is though since I've read that it was being deprecated (even though the date says April 9, 2013).
As per the comment on the above page, there is another project known as Qt-Jambi which does basically the same thing: http://qt-project.org/wiki/Qt_Jambi
Here's a really outdated Java binding for wxWidgets http://wx4j.sourceforge.net/.
As a side note, Processing has its own GUI libraries with ControlP5 being my favorite. You can find it here: http://www.sojamo.de/libraries/controlP5/