I am writing a story of a slice of life of a teenager girl who seeks her forgotten past and run away from her forced marriage to follow her dreams. I want to add another story of her cousin and her best friend who gets pregnant early in age. Would it be too weird if I do so? I want to add some points of teenage pregnancy in my book, but this issue relates nothing with the main character or her story except for the point where the main character is seen to be with her cousin in the difficult situations. Should I do this? Should I add this another story of second lead in the book?
Connection is important
Your notion that the two stories don't connect is problematic. I think some kind of connection is important.
The two stories need to have enough connections that they can authoritatively answer the question; why are we seeing both stories, and why are they in the same book and not in a book each?
It doesn't have to be more than a thematical connection though. One story could comment on another story, preferably in order to strengthen the theme and message of the book.
For instance, isn't teenage pregnancy a possible consequence of forced marriage? If not, you might want to make it so in this story... Maybe you're on to something when you want to add the other story?
The strong connection
You can also make the connection between the stories really strong.
The runaway's story could be mirrored with that of someone that did not run away. You can use the two stories to show parallel possibilities. What would have happened to the runaway if she'd stayed? What would have happened to the cousin if she'd run away?
The stories could be connected more than that.
In the beginning
You could start with one perspective in one story where both POV-persons were present and then split off into two separate stories. Perhaps when the runaway ran away?
In the middle
As the stories progress, find as many touchpoints and connections between them as possible. You might have the two POV-characters communicate, or have one character's actions affect the other. Or you may arrange your scenes so that they mirror each other. For instance, showing similar events in the two POV-characters' lives and how they differ. (Check out Sliding Doors for an example of parallel stories, albeit not exactly of the kind I'm talking about here.)
This, of course, has the potential to be a great help with your message and theme. The difference will say a lot...
Make the two stories intertwine as much as possible in order to always answer why both stories are included.
In the end
One thing I think will really drive home the need for both stories is to make them converge in the end. Show that they both are needed to get the ending of the story. Preferably in such a way that both POV-characters are once more in the same scene, both taking part in the climax. Maybe the actions of one character caused the climax that is really bad for the other character? Find some reason for them to be together again.
Theme and message will tell you if you should do it or not
What is the message and theme of your story? Can these two plots be used to deliver that message and convey that theme? If so, go for it!
If your message and theme cannot be contained in both plots, you probably should either change the message and/or theme or drop the cousin-plot.
Another possibility is to connect the two stories serially. I.e. the cousin plot is book number 2 knocking on the door wanting some attention, while, in fact, it should be the sequel to book 1.
Personally, I believe that it would seem kind of weird in the same story, and if they do not overlap/are completely separate, I would not recommend writing about them in the same book, but here are some options you can do if you want to include them both.
Write them as two separate stories and note that they take place in the same world (mention characters from the first book in the second and vice versa).
Find a way to connect the stories or show the cousin/friend's story in passing or as a chapter of the main story. Example: While I was walking down the street, I wondered how my cousin [Bob] was doing. Last I heard... (insert story here & replace Bob with the actual character name.) Of course, you would probably have to find a better way to put that, as I am not a very good writer, nor do I know enough about your story to write a good example.
Write the different chapters in the perspectives of different characters and then merge the stories at the end through some commonality. Example: Chapter 1: Main character. Chapter 2: Main character. Chapter 3: The best friend. Chapter 4: The cousin. Etc. And at the end, they would all appear or affect each other in some way.
Find a way to incorporate teenage pregnancy through a character in a way that is relevant to the story itself, so that readers are not constantly wondering where you are going with the story. Fairly self-explanatory, this can go with one of the other options as well if you choose.