what piece of hardware do i need to "double" a rca signal into two rca signals

You’ll need something to split the signal. You can use 3 Y splitters - 1 input 2 outputs - or you can use a powered splitter which will do the same thing but will use its own power source to make sure the signal is split without degrading the quality.

This guide has links to all of the equipment you’ll need as well as the steps to set everything up if need it.

if you have a capture card with passthrough (look for an output slot), you can just plug another set of cables into the card's output and into your TV.