A relative velocity is not a velocity of an object, or even a velocity at all. A relative velocity is a measure of changing distance between two objects.
In addition to your difficulty with the definition of "velocity", you are also confusing yourself by working with too many objects and reference frames. If the two cars or two rockets are stationary with respect to each other, you don't need to have both in the thought experiment.
The problem is that when a rocket is alone in space with nothing around from which to measure its speed, it can
define its speed to be literally anything between zero and C. However, doing so establishes a reference (synthetic, but still valid) from which to measure changes in speed. Then when it fires its rockets, it measures a change in speed with its accelerometer and a clock, and can calculate a new speed.
But see, since the initial speed can be arbitrarily chosen, the acceleration doesn't help you pin down an absolute speed. It shows that while acceleration is absolute, but speed is not.
A relative velocity is not a velocity of an object, or even a velocity at all. A relative velocity is a measure of changing distance between two objects.
You are trying to
define yourself as correct. You can define yourself as President of the United States if you want, but that doesn't make it true so good luck getting anyone else to agree!
Besides which, there is no need for such a game. To eliminate ambiguity, instead of "speed" (or velocity), we/you can just say "absolute speed" or "relative speed" to make sure it is unambiguous which one we mean. You believe that "absolute speed" exists and "relative speed" does not. You are wrong (which is why scientists don't differentiate), but at least it will be easier to discuss if we use consistent and unambiguous terminology.