My brakes rotate around after I tighten them and other v-brake questions I recently purchased the long type of v-brake pads from Disco Brakes at Amazon. These are the ones with the tail.

My original brakes were the simple shorter kind, installed as small spacer/washer/brake post/washer/large spacer/washer/nut. The concave/convex parts fitting together. Interestingly enough the new brakes had the same order!

But I watched one brake repair video at YouTube, and they said there was another washer, a flat one, between the brake and the first spacer. Neither my old or my new brakes had that. Another video told me to use the big spacer first and loosen the cable to do so. Still another place said to use the washer on the post first, then the spacer that fits into it. So I am confused. What is the best order here?

As to the title of this post, it refers to a rear brake install. I installed it as listed above, because that was how the previous brakes were installed and the order of stuff on the new brakes. I tighten it down, and the brake is rotating around! The front ones stay in place, but even though it is tightly screwed to the brake post, that one rear brake is able to rotate around!

I will check the post in the morning, make sure it is not a flawed brake pad. But if it is not, I would like to know what to do with this very strange issue. I can switch the brake for one of the fronts and see how that works.
Either spacer arrangement is acceptable, and the choice is part of correctly installing the new pads. But I'm not clear exactly what pads you have, as there are two types: one with posts that poke out and bolts at right angles that clamp onto them (older style) and pads with threaded bolts built in that attach directly to the V brake arms.

Typical V brakes should have the arms vertical when the pads contact the rim. The specific requirement is that the pad surfaces are parallel to the rim at that point, and as they wear they will become that way. Those semi-spherical spacers and washers allow you to rotate the pads to achieve that, so you have some tolerance there. That also lets you toe in the pads, BTW.

It's better to have the arms slightly out past vertical with new pads because as they wear the arms will move in. But that should be by a small amount - a couple of millimetres at the adjustment point marked L in the diagram below.

The flat washers shouldn't need to be against the brake pad, normally they're used under the nut to help isolate rotation of the nut from rotation of the pad (so you don't move the pad out of alignment when you're doing up the nut).

 (image from Saccom)