It would be great if we could select Object 1, and then select Object 2 on the same or different layer, and then have Object 1 be sent to right above or right below Object 2.

This would ideally be done with a shortcut like CMD+Shift+[ and CMD+Shift+] and could be done regardless of what layer Object 2 is on and whether or not Object 1 is part of a group or a clip group.

Larger, more complex illustrations often have many layers and many shapes, lines, groups, clip groups, etc. (Sometimes hundreds, even thousands of objects!) In order for those illustrations to look good in the end, the user has to carefully manage which objects are in which order, but the more objects, the harder it is to figure out where in the pile the object should be. This means more time spent doing a task that is likely to cause frustration, instead of starting on the next great illustration.

At the moment, the options that exist are either too big of a jump (Send to Front, Send to Back) or too small of a jump (Bring Forward, Send Backward) to address this specific use case (although Send to Current Layer gets closer).

Adding this feature would go a long way in improving layer management within Adobe Illustrator.