That's where I lost you.
The GTX 560 Ti reviews I've seen have shown nearly no gains for the 2GB part vs. the 1GB part:
http://www.techpowerup.com/reviews/P...0_2_GB/31.html
The effectiveness of GPU memory size is a lot different than main system RAM; most GPUs have a "sweet spot" where throwing more RAM on them may be cool, but doesn't help much. The HD 6950, for example, can use 2GB at 2560x1600 and high AA, while the 1GB version runs out of steam:
http://www.hardocp.com/article/2011/...mance_review/4
2D on a second screen while 3D gaming on the main screen is something I've never seen tested, but the 2D load should be next to nothing.