Recording Video From one PC to Another
In order to duplicate the display you would need extra hardware in your machine anyway, otherwise you will still get lag, so I would instead recommend simply upgrading your existing machine - it will be cheaper, and the spinoff is that you will have a better machine.

The machine I am currently writing on has a reasonable GeForce graphics card, quad core i5 and 8Gb of RAM - pretty cheap, but can happily use FRAPS on full screen (1600x1050) at >25 fps while playinng COD4 or MW2 for example.