How could he stand us being far away from each other?
The phrase only has 2 Google hits. So I suspect the phrase isn't very common. What's a better alternative?
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The sentence is perfectly valid and isn't an idiom. Cambridge defines "stand" in this sense as:
to successfully accept or bear something that is unpleasant or difficult
I don't think that it is an idiom or phrase of some kind. It is just a simple English sentence, and can be rephrased as:
How could he be okay with us being far away from each other?
The word 'stand' from the original sentence is replaced with 'okay with' in the above sentence. Clearly, each word stands for itself. Hence, the phrase in itself is not an idiom of any kind.