First of all, in Portal 2, it's clear that Caroline is inside GLaDOS: 1. In the underground, Cave mentions that if he doesn't make it, they should put Caroline into the AI 2. In the end, GLADOS actively deletes Caroline as her personality
Now, for this theory, let's assume that Cave and Caro are Chells parents. For the theory it's a minor thing, but it works out better.
GLADOS has a really similar personality to Cave Johnson, after he got poisoned by moon rock dust. Also Cave wanted to live along in the AI, if it would be possible to store a personality on a disk, before he dies. Assuming that Caro is inside GLaDOS, he probably died before, but it's never clearly proven.
Now maybe Cave really was able to put his personality into GLaDOS, but because he still loved Caroline, she also got put in anyway. While Caros personality is stored in GLADOS core, Cave rests in her Body.
In 2010, Chell awakens in the relaxation center. She looks about 30 years old, so Cave and Caro could be her parents before they died. The Part of Caroline made GLADOS take care of Chell, while Caves' Personality made her kill all scientists, cause they didn't work in the way he liked it, also he slowly turns into a psychopath, cause the moon rock triggered something that changed him (between the last underground message and his death there was still some time to get more and more insane).
Chell wakes up and Cave made her go through the facility, not caring for anything anymore, not even his daughter. Caro couldn't do anything against Cave doing that to her daughter, cause Cave was the more powerful Personality. When he tries to kill her in the incinerator, Chell destroys GLaDOS.
In Portal 2, GLADOS gets rebooted and Cave is still the more powerful personality, so he continues to make experiments with Chell.
And now why I believe this theory: When Wheatley got connected to GLaDOS' body, he also acts insane pretty fast. He's just a core that should slow down GLADOS, so he's not evil by default. But if Cave controls him, it's plausible. Meanwhile GLADOS turns "good" within seconds. She sarcastically complains about your mistake, but she's not threatening to kill you. That's because now it's only Carolines personality. Later when GLADOS gets back plugged in, she seems to delete "Caroline", but that's only a lie. She cares about Chell as her daughter, and so she deletes Cave. But because Chell doesn't know about Cave being her father, who did all this to her, it's said that "Caroline" got deleted. And Wheatley was nice again and really sorry what he did to Chell after he disconnected from GLaDOS' body again
In the Coop mode, she's sarcastic again, but not as much as with cave before