Why does G-d opt not to relay Sarah's message exactly as she said it? What is G-d trying to teach us here?
Judaism has a great level of respect for the truth. Lying lips are anathema to G-d (Proverbs 12:22). Pirkei Avot (1:18) teaches us that truth is one of the three pillars upon which the world endures. There has to be something markedly potent to override something such as truth.
I'm sure you have met at least one person who likes to "be brutally honest." They are the type that like to "tell it like it is." Regardless of their level of intelligence, what these sort of people forget is not only that to be human is to err, but also that our perceptions, biases, and experiences are more than capable of obfuscating an objective view, and it takes a lot to overcome that. It is a self-confidence that crosses the line and turns itself into arrogance. Most of us don't consistently do this to the point where it makes me wonder about whether the individual has a superiority complex. But L-rd knows that just about all of us have had that moment where we feel the need to be brutally honest, even if it's necessarily not to stroke one's ego. That is the type of moment Sarah was having here.
Sarah had the right to be frustrated, and this excludes what she went through on Abraham's adventures throughout the Genesis narrative. She really wanted to have children. Abraham had to have a child with their handmaid, Hagar, because her childbearing prospectives seemed that hopeless. Plus, they weren't getting any younger. Let's be mature here for a second. Sarah was well past menopause. Without the miracle worker known as Viagra, Abraham could have either been suffering from erectile dysfunction or shooting blanks at this point. In this case, it's not as if Sarah's laugh was a baseless act. There was some pent-up anger, hope, and frustration all bottled up there, and a good laugh seemed to be the way to go, even if the news of a child was in complete disbelief.
Maybe Sarah was perfectly justified in her reaction. She certainly had reason for skepticism. Even so, G-d decided not to relay the message verbatim. Honesty is not an absolute value in Judaism, and we see that in the halacha. Even if a bride is absolutely hideous, you are to tell her on her wedding day that she looks beautiful (Ketubot 17a). If you're eating at someone else's house and the food does not taste good, you are permitted to lie and say the food tastes good (Eruvin 53b). If people are in the middle of a conflict, you are permitted to lie and tell the parties that the other party holds them in high regard and that they wish to make peace, provided that you have basis to believe that this will actually work (Yevamot 65b). In Pirkei Avot 1:12, Hillel said that one should be a disciple of Aaron by loving and pursuing peace. According to Rashi's and Bertinoro's commentary on the passage, Aaron was such a pursuer of peace that he lied to accomplish it. Within this commentary, there is a parable of a quarrel between a husband and a wife. A man told his wife that is was forbidden to have marital relations with him until he spit in the eyes of the Kohen Gadol (High Priest). Aaron talked with the wife and said that his eyes hurt and her saliva was the cure, thereby resolving the marital dispute. Aaron believed in pursuing peace so much that he allowed himself to be insulted and degraded in the process, which would explain with R. Isaac Alfasi concluded that telling a white lie for the sake of peace was a mitzvah!
An omission of truth or a half-truth should be told before a downright lie, and we should recognize these moments as exigent circumstances, not as a norm to permit lying in all cases. Even so, we better understand why Maimonides said (Misheneh Torah, Hilchot De'ot, 5:7) that one does not "alter the truth in speech, not adding or subtracting, except in interests of peace and the like," and why the Chofetz Chayim permitted the telling of a lie because of peace (Laws of Rechilut, 1:8).
Judaism is not about truth for truth's sake, particularly when it is at the expense of another's dignity, and it's not about "following the halacha for halacha's sake." Halacha is supposed to spark something within us. It is supposed to make us into better human beings and help the world be a better place than we left it. The words we use are vital tools in that pursuit. Our ability to use words is one of the features that distinguishes us from animals. If serving G-d means that you have next to no regard for human dignity or how one's words will affect another, even if you're "being brutally honest," then you do not understand what it truly means to serve G-d. We can choose words to knock people down or lift people up. Jewish tradition decidedly teaches us to pursue peace by using our words to repair damage that has already been done, lift people up, and help the world realize the significance of properly treating people that are created in His Image.