How can I follow a structure that is flawed and you realize in the middle of the case that you’re wrong?
Following a structure that is flawed from the beginning
once you recognize your structure is flawed, you should not follow it anymore. The ideal thing in this situation is to tell the interviewer you recognized some elements should be added/modified in it, ask 1 minute of time, change what needed and finally present and proceed with the updated version of the structure, including the relevant elements missing before.
I will restructure both of your questions into two use-cases:
1) If you are talking about the initial structure:
I suggest asking an interviewer something like: "Is this structure good to move forward with? Am I missing something or is there anything I should prioritize?" I recommend doing that both in candidate- and interviewer-led cases.
2) If you are talking about a structure you make while solving a case:
You simply take 30 seconds and make a new structure. It's important! Don't take 30 seconds and come up with 1 hypothesis (random guess). When you take additional time - always draw a new structure and present it to the interviewer.