San K said:
when they are in same frame of reference there is no disagreement.
In classical physics as well as in SR, they are always in the same reference system; as a matter of fact, they are always in an infinite number of reference systems.
Is that clear to you so that it's just a matter of formulation, or are you perhaps not familiar with the definitions of classical mechanics?
[...] i.e. we can make either of A or B to be correct, in a sense, depends upon who moves ...assuming...only one of them is allowed to "move" (back into others frame of reference)
Whatever inertial reference system you choose, the prediction will be the same.
For example:
1. As determined with a system in which the "stay-at-home" is always in rest (approximately):
- Nearly all the time the traveler's clock appears to be slowed down due to speed.
2. As determined with a system in which the traveler is in rest during the first leg:
- Nearly all the time the stay-at-home's clock appears to be slowed down due to motion.
- during the second leg the traveler appears to move much faster than the stay-at-home, and his clock appears to be much more slowed down.
Calculation shows - as it ought to be - that the results of both descriptions are the same.
Harald