Are you sure that changing the resolution of your game is what you want? In your original question you were rather talking about scaling the objects within your game, i.e. fixed size vs. relative size.
If changing the resolution is what you want there are multiple ways to do that, but I’m pretty certain that dynamically changing the resolution does not work on all platforms (Windows, Linux, Mac OS X) equally well. A lot of work has gone into this issue in the past (link), but I’d still recommend writing new configurations to a config file and telling your users to restart the game (as done here). As a default, either start your game in windowed mode at a rather low resolution that modern screens all support or request all possible resolutions from your user’s screen and set the maximum one fullscreen.
I could provide code snippets.