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is it possible to Update the INS (DME Update) while we are navigating or do we have to couple the ins off first?

Good question. They recommend to uncouple the autopilot (with e.g. reverting back to HDG select) for the time the unit starts the DME update. Reason is that the update may cause more or less severe heading corrections which would harm passenger comfort.

Now that seems to be a recommendation for the rw units and also for the case of a huge offset already having developed. In the sim, I never saw huge jumps or something, so you are safe to leave the autopilot in NAV and then start the DME update.

The CDU itself can do both things, deliver the signal to the AP and, at the same time, process the DME update correction. So even a single INS installation is stable enough to perform both tasks at a time.