Max's mom likes to type up Max's stories in story book format. If he were to retell his adventure to her, it would end up like the source material.
At one point, when Max and Carol are in the desert, Carol gestures at the sand and says something along the lines of 'This all used to be stone', indicating that their world was slowly falling apart. And what pours out of Douglas' arm when Carol tears it off? Sand. I felt quite smug when I noticed that.—Draele
Though I've seen some people mention this, a lot of people missed it, too. A line Carol says to Max when he's showing him the island is You're the owner of this world, Max. Earlier in the movie when Max is in bed after messing up his sister's room, you see a globe given to him by his father with the same words as it's inscription. This set the ball rolling for me to understand that Carol represents his dad and Max is dealing with the divorce of his parents. There are other examples but that was the big one for me.
Carol might also have traits from Claire, Max's sister: the heart Max makes for him seems to echo the paper heart 'To Claire, From Max' that he ripped apart at the beginning. Meanwhile, KW acts very motherly to Max, and her relationship with Carol is reminiscent of people who still love each other but can't stand each other anymore.
The story Max tells his mother in the beginning about the vampire who lost all of his teeth is extremely similar to the dialogue between him and Carol about it being like your teeth falling out. You could also interpret this as another version of the entire movie.
The line said by K.W. while she says goodbye to Max is from the original story, but said in a completely different tone which was perfect. The line being Don't go, I'll eat you up - I love you so.