Splitter is just that, it splits the video once it leaves your video card, anything attached to that will get the same image.
What connection are you using exactly for the second monitor? Why not just run VGA cable to the TV instead of the RGB cable. If it's an LCD TV they should all have a VGA input. Your issue is that you are degrading the signal and RGB is not designed for HD images, unless you are talking about Component video (3 color cables to an HD input). But even component will have some issues (from wiki: "Component video connectors are not unique in that the same connectors are used for several different standards; hence, making a component video connection often does not lead to a satisfactory video signal being transferred. Many DVD players and TVs may need to be set to indicate the type of input/output being used, and if set incorrectly the image may not be properly displayed. Progressive scan, for example, is often not enabled by default, even when component video output is selected.")