I hesistate to play the Bard's pedant, but it's "in" this mortal coil. "Mortal coil" has reference to one's body. When one dies, his spirit shuffles off its coil, i.e., leaves the body.
Another common piece of fractured Shakespeare is "hoist on their own petard." A petard is an explosive, a bomb. Thus it is properly written "hoist by their own petard." Ask Rosencrantz and Guildenstern.
Before one shuffles off his mortal coil, before life's brief candle is put out, one should take time to read--deeply read (and occasionally memorize) and recite--Shakespeare. All of it. Even Titus Andronicus.
You and I disagree on a lot, but my English geek thanks you for that.
I will ponder that one. To me, it means a place, that an inner being. Thanks for you kind note.
Done that. But, seriously, you can skip Timon of Athens.