Have you been or seen this sort of issue before whilst doing your PhD?; the authors of a paper were in a situation such as:
(1)the arrangement of the authors cannot be agreed, so there were conflicts going on.
(2)the first author should be X, but Y got it; again conflicts arised.
(3)X didn't get authorship but did most of the work; same as above.
(4)anything you've seen or experience.

How was it solved and how would you handle it if you were in the situation?

Although it doesn't usually end up in fist-fights this is a fairly common issue, so I'm surprised that you didn't get any answers to this question. Here are some widely used and fairly reasonable guidelines that you can invoke and might get people to (reluctantly) agree on authorship issues.