I was wondering if it's possible to embed a MonoGame instance not in the standard window, but rather in a GTK# widget. If yes, how could I do it? Do I have to write a custom widget? Is it even better to switch to OpenTK even though it seems quite counter-productive to me?
it's possible, but a little trickier than vanilla winforms MonoGame. There's a good tutorial here : http://www.oldschoolpixels.com/?p=390
Switching to OpenTK is not advisable. MonoGame has a lot of things that aren't in OpenTK when it comes to texture loading, entity management, etc.
Think of OpenTK as a relatively barebones way to talk to OPENGL from .NET