Excerpt from a book (I'd prefer "An excerpt from a book" or "Excerpted from a book", but grammatically, yours is correct.)

I believe that everybody in the world definitely has the most beautiful moment in his life.  

When is this sentence happening?  Are we speaking about now?  or something in the past?  As written, the most beautiful moment in his life is happening at this moment.
I think you want I believe that everybody in the world is definitely having the most beautiful moment in his life.  or I believe that everybody in the world has had the most beautiful moment in his life.  The second sentence means that the "moment" happened and finished in the past.   

A situation that could never be forgotten.  I prefer "A situation that couldn't be forgotten." but that's stylistic as "never' emphasizes "never" and using "not" emphasizes "forgotten".  

Whether it's about love, family, friends, or whatever it is that makes us happy.  Ooops... I made a mistake... This IS a grammar error.  This is a sentence fragment.  It needs to turned into a sentence by attaching to another phrase.  It probably should be attached to the preceding statement.  A situation that couldn't be forgotten whether it's about love, family, friends, or whatever that makes us happy.

But, when that the most beautiful moment comes, people more often in a situation of two-timing on God.   Eek... Another grammar error.  Your last phrase lacks a verb.  Here's a possible correction.

But, when that most beautiful moment comes, people often are cheating on God by .... I added the "by..." so you could fill in exactly what you mean by two-timing.  I'm guessing that you want it to say something like "by ignoring the most beautiful moment."

Quoted and translated from an Indonesian book.