If you are going to enforce the "having another review", than you need to hold the manuscript, go get the review and not have the authors do an edit. It will disrupt things too much if they revise from what they wanted and A disagreed with, if C likes it (maybe they stand their ground then). Or if there is some other clash, synthesis of changes needed, etc. Don't send it to them early and then have the kerfuffle later...and definitely don't spring it as a surprise.
You might send them a note saying that you need a little more time (at least then it is not in a black hole and they are less likely to pull the paper).
If at all possible, I would read the paper yourself and see if you can just pass it without the need for the extra review. At least to the point of getting it back to the authors. But when you read it, you have to make a judgment call if you feel OK about it. And yes, I realize this might be "breaking a rule" from your three bulleted scenarios. But many journals and editors are capable of inserting a little judgment.