Complex cable animation issue I'm making a cable animation.

The first attempt was to use curve modifier, but the issue here is that the connector gets deformed as well.
I've tried a different approach, by separating cable to parts and making connector &quot;follow the curve&quot; with constraints. 
And now the connector and main part of the cable (red) are fine. But I can't get the tubes (green) to align to the holes of connector. I've tried to rotate it and so on, it's always misaligned at different points of the animation.
I've also attempted to use hooks to connect tubes to the connector, but it works only for short distances and doesn't fit the goal.
Any other approaches I can try?
Edit: So my solution is not completely accurate, because as you say the big cable and the tubes do not join at the same point of the plug.
*Create an empty at the cable end, select the empty, shift select the cable, go in Edit mode, select 3 vertices, press CtrlP:

Parent the plug to the empty:

Give the cable a Curve modifier, move the cable along the curve: