Your pictures didn’t show up for some reason, but you mentioned an extension that can detach and is controlled by the partner joystick. If this extension, after detaching, will remain physically connected to the main component of the robot by any means, even by a rope, it is legal. However, if it completely detaches such that there is no physical link to the main component, and does so on purpose, it is no longer legal.
Great. Two in one day? Seriously?
For the original post, I think what you are talking about is known as a “tether-bot.” Basically 2 robots in 18" by 18" by 18" that split off at the start of a match with a tether connecting them. As long as the tether connects them, it is still legal. Use the search function on the forum and you will find some good examples of this.
I will add that as long as theirs only one Cortex on the tether-bot then it should be legal.