I work in a juvenile detention center, we have a rotation schedule. Is it legal for us to work 8 days in a row, and to be mandated to work on some days 16 hours? Also what is the law on mandating? How often can you be mandated?

Michigan has no laws regarding number of days in a workweek or the number of hours in a day you can be required to work or the frequency with which you can be required to work them.

In Michigan, and in most other states as well, you can be mandated to work 168 hours a week, every week. It would be stupid, but it would be legal.