@layman,
This has nothing to do with SR.
You are misunderstanding a principle that was well understood hundreds of years before Einstein.
The example you are giving is completely solvable using Newton law's. In fact, Newton in Principia wrote that the laws of mechanics are equivalent under any inertial frame of reference.
Let's consider two reference frames (you aren't going to like this, but this is basic Newtonian Physics that we teach in high school that has nothing to do with Einstein).
1. In the first Newtonian (i.e. inertial) Reference frame, we consider the Earth motionless. The rocket starts out motionless, then let's say it accelerates (this is a net acceleration including gravity) at 100 m/s/s for 30 seconds. After this time we would say that the rocket is going 3000 m/s. (The earth would have orbited... but we can simplify this, I will add the mathematics if you would like.
All of Newton apply in this frame of reference. V = V0 + At is true. If we want to calculate the force, we can use Newton's laws for that.
2. In the second Newtonian Reference Frame we consider that the Earth is moving (downward from the perspective of the rocket) at a speed of 3000 m/s.
The rocket accelerates at 100 m/s/s upward for 30 seconds. After this time the Earth is still going in the direction we call "downward) at 3000 m/s, and the rocket has a velocity of 0 m/s (it is motionless).
The point that Isaac Newton made is that either of these inertial frames of reference are equivalent.
All of Newton's laws apply to the second frame of reference as the first. V = V0 + At is still true. Newtons first, second and third laws all still work.