Living in the rational world carries a couple of burdens: you have to discard the comfort of "knowledge" from religion, and become comfortable with both "Shit happens" and "I don't know" as legitimate answers.
And let me tell you, I hate "I don't know" as an answer. That was the hardest part for me, not being able to fall back on "goddidit" or "that's just the way it is" (which is a plausible, but no more satisfying, answer).
But, the simple fact is, the universe is under no obligation to be immediately explicable. It needs to be picked apart by cleverer people than most of us here, and even that knowledge is provisional. That said, the entire history of inquiry is that of always honing in on the best available truth, sharpening it every year, moving always closer to a more complete understanding of the universe around us.
And personally, that's where I find some of my favorite coping mechanisms: first, in the knowledge that there's a discovery out there that just might blow my mind tomorrow; and second, that I can go outside and look around and know -- in outline, at least -- how everything works.
Considering how huge the universe is, and how limited a brain I have, I find it a really comforting thought that I can pack a general understanding of all those cubic lightyears into the meat computer balanced on top of my body.