Obviously if you put the current itinerary up and your preferred outcome you will get more precise information. Hypothetical questions get hypothetical answers.

Cancelled segments can be removed, and separately from that there is a 300 mile rule that would allow you to start from say BHD compared to DUB. If your ticket is DUB-LHR-[lots of places]-DEN-[few more places]-LHR-DUB, then there is some leeway to make it say LHR-DEN-LHR if DUB is cancelled by BA. But you can't preserve the DUB-LHR-DUB and then have, as a separate set of flights, the DEN sectors. You said earlier the AA flights are the ones cancelled, so that won't allow you to muck around with the DUB flights. But the cancelled flights on AA would allow a refund, and starting again, to give one example among the many remedies. If was just the cancelled AA flights involved then it may be easier to resolve after starting the trip and in direct communication with AA. But if DUB-LHR-DUB is still operating then your options are going to be limited.