Sounds like a Best Buy laptop >3>;
Firstly, it says you have the 3GB of video memory because it's shared with your RAM (computers only ever use up to 5GB of the RAM, so the left over is shared with your VPU/GPU)
Secondly, have you tried doing a clean instal of your drivers? That can sometimes help.
Thirdly, the reason it says there's 2x 6500M's, is because the 6720 is a Crossfire (SLI, combination, fusion, etc) of two GPU's in one. I think it's the 6650M and the 6520, which is why it would say you have a 6500, because the 6520 is OEM and isn't exactly standard-issue.
The problem is that one of those is an intergrated card, the other is a dedicated card. And the video problem means that it's just running on the intergrated card, which I'll bet is the 6520.
What you might want to do, is go to Device Manager and go under Display adapters. Mess around there and see if you can prioritize one of the chips. Preferably the other one, the 6650M