A: Go back to Vienna if you have to, but this time, I’m not coming with you. You’re on your own, Randy.
Can I use “I’m not going with you” in this sentence?
I don’t really understand what the difference between I’m going and I’m coming.
Why are the two people in the same place, and talking about the other place, still using “coming” instead of “going”?
Interesting question. Both are OK. I think “I’m coming with you” is just a very common thing to say when someone else is going somewhere. You can say “I’m coming with you to the gas station” or “I’m going with you to the gas station” with little difference. But if you just say “I’m coming to the gas station” it sounds like you’re talking to someone who is there, or will be there.
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The main meaning of ‘to go’ is to move from the speaker: go there!
The main meaning of ‘to come’ is to arrive, to move towards the speaker: come here!
But in the colloquial language both verbs are often used interchangeably.
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I think the point is that the word “come” most likely refers here not to the speaker himself and not to the place of appointment, e.g. Vienna, but to the friend who is going to go there
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“I’m coming with you” - more emphasis is on the action of accompanying you.
“I’m going with you” - a little more emphasis on the act of going, perhaps.
But both are fairly interchangeable.
If the speaker is moving towards Randy, she is coming. If she is moving away from Randy, she is going. But if Randy is beside her and also moving in the exact same direction at the same speed, then she is coming and going at the same time, thus you can use either word 
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