Not knowing all of the details of your situation, this seems like the kind of thing working agreements are supposed to help with.
If you can get the parties involved together, you may be able to come up with some explicit guidelines for communication. For example: “assume good intent.” This would apply to you (you will not assume that your CS are personally attacking you) and them (they will not assume you are indifferent to the customer). If either party steps out of line, you can come back to the working agreements, point out that this is not how any of you want to work, and hopefully correct the behavior, or else resort to discipline in the case of repeated violations.
Hope this helps.
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