On the left is the chamber which will house the parachute and the plug which will launch the parachute. The chamber will attach to the rocket car's body/tube by inserting the long end into the tube.
On the left is the draft version of the plug which launches the parachute. On the right is the final product. I chose to make it spherical so that it can move freely within the parachute chamber.
Just for fun, I created a decorative piece for the rocket car's body. It features a cute monster face and is designed to fit snugly around the rocket car's body/tube.
This is an assembly featuring all three pieces that I designed demonstrating how it may look once the rocket car is assembled.
This is a screenshot of all three pieces inside of PrusaSlicer before printing.