Another apparent special relativity paradox involving three travelling radioactive containers I've got a question concerning the special theory of relativity.  Once again twins paradox, but somewhat more complicated.
That is one-dimensional problem and gravity is neglected. Acceleration/deceleration are present but not always mentioned.
Suppose, before take off of a spaceship from Earth, it was loaded with three containers X, Y, Z of freshly made isotope. Concentration of decayed atoms are x0 = y0 = z0 = 0.  When the spaceship reaches constant velocity V relative to Earth, concentrations of decayed atoms in containers are equal, x1 = y1= z1. Now, the spaceship is an inertial system of coordinates, and we use it as a reference point.
Container X stays on the spaceship, while containers Y and Z are immediately loaded into small identical rockets. Container Y is sent forward with velocity V relative to the spaceship. Relative to Earth it reaches constant velocity V <  Uy < 2V. It moves in this state for a time Ty in its own reference frame. This time is arbitrary larger than the acceleration time.
Container Z is sent backward with velocity V relative to a spaceship.  Relative to Earth it reaches constant velocity Uz = 0 and stays like this for a time Tz = Ty in its own reference frame.
Then, containers Y and Z are returned on the spaceship.  Because relative to spaceship both containers performed equivalent journey, concentrations of decayed atoms should be now y2 = z2 < x2. This relation should hold from this moment on.
But when spaceship returns to Earth, this relation is hard to to explain. Because relative to Earth containers X, Y and Z performed partially different journeys. Barring common parts and accelerations and using now Earth time, the round trip time Tr is the same for all three containers. But container Z spends most of this time with zero velocity Uz, container X spends most of this time with velocity V, while container Y spends  most of the time with velocity Uy > V. Accordingly, upon return to Earth concentrations of decayed atoms should be y3 < x3 < z3.
What am I missing?
 A: The first point I should make is that the effects in question will be the same whether you use decaying isotopes, clocks, or any other mechanism or phenomenon that happens with a certain time-cycle. What you are asking, is whether time will have passed at a different rate for X, Y and Z.
You are right in pointing out that when Z sets off backwards from X it is stationary relative to the Earth, while Y spends that period moving away at twice the speed of X, ie 2V.
What you overlook, however, is that for Z to return to X it must reverse its motion and go for a time at twice the speed of X, ie 2V. Y on the other hand, will reverse its motion to return to X, during which period it too will be stationary relative to the Earth. So you see that, contrary to your initial impression, relative to the Earth, Z and Y each spend exactly the same amount of time stationary and moving at 2V, they just do so on opposite legs of their journeys.
As a result, relative to Earth time passes at the same overall rate for Z and Y, which is what X observes too.
