I can see that the scenario you are bringing up is similar to the one in the mini sim 2. Personal differences will always occur, but the as a Project Manager you need to make all your team aware that in the work space, it is mandatory to finish the project on time and with good quality. Personal differences usually lead to communication problems between the people who suffer it, so I would create a meeting between me (PM) and the people who have the differences. In the meeting I would explain that there is no space for arguing between team members
My father says that it is not what you deliver but how you deliver it. If I have a conflict with a team member in regard of vacation problems, then I would simply talk to them ahead of time and try to work something out for both parts. Communication is key when doing a project.
Let me know what you think!

Sincerely,
Roberto Pineda.