Why do you need to measure the speed of light in two directions?

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"my point is that even if both A and B are inertial reference frames, that does not imply they are stationary relative to each other. They may be moving together or apart at a constant rate, or one or both may be free falling with a net acceleration between them."

It's even worse than that Bahama :)

The definition of something being 'at rest' in relativity is that it has a uniform motion, nothing more.

You don't have any 'acceleration' at all in uniform motion, and your relative 'velocity' (I won't use speed here as that says nothing about a direction) doesn't mean a thing as I understands it for defining yourself as being 'at rest' relative something else.

There is no 'universal resting place', only relative ones. And what differs being 'at rest in a uniform motion relative being 'at rest' in a acceleration is that in a acceleration you know that you have inertia/gravity acting at you locally, constantly or intermediately, if now that is the right word to use?

If you introduce a third reference frame from where you define two comoving uniformly moving objects to be 'moving', you might do it relative a third frame, as the 'universe' at large for example. That doesn't change the fact that both can define themselves as being 'at rest' relative each other.