The Dock was moved to the right side of the screen but still auto displays when cursor on bottom

As far as I can find, putting the Dock on the left side of the right monitor or the right side of the left monitor can't be done.

But let's look at other possible solutions to your problem. Point #1 notes that you don't want the dock on the right because it would interfere with disk icons on the desktop. And when you first drag the Dock to the right side, it does indeed cover the disk icons on the right side. But if you select "clean up" on the Desktop once the Dock is positioned on the right, it will move those icons over to make room for the Dock. This is a temporary solution, however, because newly mounted drives will still be buried by the dock. If you select "clean up by name", however, then newly mounted drives will fit into the grid created and not be covered by the Dock.

Not the solution you were looking for, I know, but it might be a workaround.

Are you using a trackpad by any chance? I too thought the way the Dock popped up on different monitors was completely arbitrary or broken, until I found out how it actually works:

• If you move the cursor to the bottom edge of either screen and keep your finger on the trackpad, the dock will pop up right away
• If you flick the cursor to the bottom edge of either screen (removing your finger from the trackpad as you finish the movement), the dock will not pop up

This is designed like this intentionally so that as you're mousing around in full-screen apps, you don't inadvertently trigger the dock when you use controls at the bottom of the full-screen window.

It actually works really well, once you know how it works ;-)