Effective military scheduling

The thing about "upset at being relieved from duty" and "depressed from long patrol duty" at the same time is a known bug. The problem is that going on break doesn't actually reset or decrease the counter of how long the dwarf has been on duty, so when he goes back on duty, he thinks he's been working for an ever-increasing amount of time.

Having orders with fewer than 10 minimum should fix this, but it has its own problems. As you note, it does count as being "relieved from duty", which is a problem if your military dwarfs have no civilian skills. Additionally, it runs afoul of another known bug having to do with training rotations, which causes all the dwarfs in the entire squad to be momentarily "relieved from duty" every month so that new dwarfs get a chance to participate in the training order.

The training order is pretty unreliable to begin with. Dwarfs have extremely busy lives, and often it is just too difficult for them to actually schedule a group training session. Supposedly this will be fixed sometime soon.

The only workaround I know of is to quickly train your military dwarfs up to the Elite level (with a danger room), which causes them no longer to complain about long patrol duty; then just keep them employed all of the time.