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To me, sentences like "She is not coming with us" are statements to inform what was told earlier. However, I've heard people using it in situations like this:

John: Let's get moving before the sky turns dark

Bob: Is this traitor coming with us?

John: We need her.

Bob: She is not coming with us!

Nobody has informed Bob that she doesn't want to come. It is Bob's personal opinion. My question is, is it rude to use this construction in daily conversations? Or should I say "I believe she shouldn't come with us"

Many thanks!
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>Bob: She is not coming with us!

Means here: She is not to come with with, I don't want her with us.
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Also, Bob can use the progressive tense to show his insistence. In the US, we often slow down the progressive pronunciation to give it even more emphasis.
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Comments  
My question is, is it rude to use this construction in daily conversations? Or should I say "I believe she shouldn't come with us"

My instinctive response is that it is rude and could sound aggressive. I would avoid it in daily conversation. Your suggested sentence is certainly politer. However, the context of the dialogue requires this aggressive response.
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