Mordekaiser received a rework since the previous answer was posted, which completely changed the way his ultimate works. Previously, it applied a damage over time effect that would create a clone pet of the target for Mordekaiser to command if the target died under its effects, and this could target and affect Shaco's clone.
The ultimate's description now reads:
R - Realm of Death - Cast time: 0.75sec
Mordekaiser slows the target enemy champion by 75% during the cast time, after which they're banished together with Mordekaiser to the Death Realm for 7 seconds.
Units between realms see each other as spirits, considering each other dead and negating any interactions between the two. Only the target and Mordekaiser will enter the realm; other champions cannot follow them. Everything that occurs inside the Death Realm is hidden, and all still inside are killed at the end.
For the same duration, Mordekaiser also consumes the target's soul, reducing their current attack damage, ability power, total attack speed, maximum health, armor, magic resist, and size by 10%, in addition to gaining them for himself. If the target dies while inside, Mordekaiser keeps their partial stats until they respawn.
If one of the two affected champions leave the Death Realm, because of having died or having it dispelled, the other will do so as well, but the stats will remain stolen for the full duration.
Shaco's clone, while considered a "champion" for the purposes of most abilities, is not affected by Mordekaiser's ultimate ability now. Mordekaiser will perform the cast animation, but both he, and the clone, will not teleport to the Death Realm.
Here's a gif, taken from this video, highlighting what happens when this interaction occurs:
Not pictured is that this does put Mordekaiser's ultimate on cooldown, so it is not beneficial whatsoever for Mordekaiser to use his ultimate on a Shaco clone.
Here are some facts about the various abilities:
Yorick's Ultimate Omen of Death: Omen of Death has the lowest priority in terms of revival because it does not resurrect the champion, only revives them temporarily. This means that if an ally were to die while under the effects of Zilean's Chrono Shift or Guardian Angel as well as Omen of Death, the champion would be affected by the one that prevents death.
Zilean's Ultimate Chrono Shift: Chrono Shift will always take precedence over other revival abilities, like Guardian Angel and Rebirth (Anivia's passive).
Mordekaiser's Children of the Grave: If Children of the Grave kills a unit affected by Omen of Death, then Yorick's ultimate will trigger first.
So, Chrono Shift has the highest priority. Next would be Yorick's Omen of Death, followed by Mordekaiser's Children of the grave.
Rift Myths has a video of the interaction with Mordekaiser and Yorick ultimate:
Note that Mordekaiser got a ghost because he killed the Yorick ghoul before his ultimate had timed out.
EDIT: KaelVonrik correctly points out that Mordekaiser's ultimate would be removed at the champion's death, then the champ would be revived by the Zilean's ultimate. So, no Mordekaiser ghost would be spawned. So Mordekaiser would need to use his ultimate after the revive by Zilean, but can cast it once Yorick ults as long as he kills the Yorick ghost before it times out to finally receive his ghost.
Best Answer
Rengar's ability that you are talking about is called True Sight.
This ability causes stealthed units to become visible to the champion with true sight.
Shaco's hallucinate creates a clone which is classified as a decoy pet. Which is not one of the things that true sight will reveal so while Rengar's ultimate is active he cannot distinguish between the real shaco and his clone.
If Shaco uses his Deceive (Q) this will be revealed by true sight. Jack In The Box's Boxes will also be revealed by true sight.
There are many other ways to tell the difference between the two of them, one such method is simply by looking at the buffs, the clone will not get the red/blue buff if the real Shaco had it.