Welcome!
What resolution is set on the external monitor? The 2011 model support a maximum res of 2560x1600 pixels.
From your info about the Intel 3000 chipset, I assume you have a 13-inch MBP. Please correct me if I am wrong.
Both the 13-inch Early 2011 and the Late 2011MBPs have a minimum 384MB of video RAM (VRAM). As that VRAM is shared with main memory, sometimes you will have more VRAM available if you've updated your RAM.
And that leads to three questions:
- How much RAM is currently installed?
- What version of the Mac OS is running on the computer?
- How much VRAM is available?
All three answers can be found by doing "About this Mac" from your Apple menu:

In the example, the "1536MB" on the "Graphics" ine is the available VRAM.
With that info we may be better equipped to offer an educated solution.