Ultimately, it isn't a significant textual concern whether Chell's mother-daughter relationship with GLaDOS is literal or metaphorical.
Note: this article contains spoilers.
If you were to step onto an average gaming forum's discussion thread of Portal 2, you would in very short order encounter some debate about Chell's parentage. We can hardly evade this theme with the prominence it takes on in the second game (although GLaDOS takes a potshot or two in the original Portal as well), not simply in the main dialogue but through the themes of lineage -- in its many forms -- taken on in the overarching story.
Indeed, there is a preponderance of evidence for Chell's direct relation to Caroline as well as not insignificant speculation why this could all be coincidence. There is plenty of writing on the wall -- you could say -- and not all of it from the Rat Man. Rather it has come from contributors on wiki discussion pages and forum threads analyzing everything from the tie-in comic to translated song lyrics. Even setting aside the fact that in games there is no such thing as coincidence, why would a game that is so determinedly made without fluff or excess as Portal is provide all this supporting material to no evident conclusion?
Ultimately, however, it isn't a significant textual concern whether Chell's mother-daughter relationship with GLaDOS is literal or metaphorical. The narrative across both games operates on a strongly Freudian level with GLaDOS/Caroline acting as the maternal aspect in Chell's development and Cave Johnson, Wheatley, and the other personality cores acting as deconstructed paternal figures. We could even go so far as to say that the first Portal is an entirely prenatal story, with Aperture serving as womb and the final physical confrontation with GLaDOS (and Chell's subsequent expulsion to the surface, pre-revision) acting as a traumatic analogy for childbirth. Consequently, we can view Chell's descent into the bowels of Old Aperture in the sequel as an exploration of her own pre-history, and if not literally the tale leading up to her conception, then the coalescing of factors that culminated in her involvement in the story.
As parentage narratives go, this is a fairly conventional one. Usually, however, these explorations of one's literal or metaphorical parents and one's psyche are led by male protagonists, often to some predictably Oedipal conclusion -- Terry Gilliam's Brazil and James Cameron's Avatar both come to mind. Here, however (and I am consciously playing on G. Christopher Williams's recent blog entry on a similar subject) the relationship is both highly matrilineal (the mother recognizing her daughter as rival and friend) as well as critical of paternity.
Beginning with the characterization of Cave Johnson, delivered to the player entirely by voice recordings and the remnants of his company's abandoned facilities, we gain the impression of a man whose ambition far outstripped his practicality. As Williams has already noted, Caroline is instrumental to the continued operation of Aperture in the early decades, while Johnson's chief contributions are seemingly enthusiasm and bluster.
The player is aware from the twist midway through the game that Wheatley was GLaDOS's Intelligence Dampening Sphere, "the product of the greatest minds of a generation working together with the express purpose of building the dumbest moron who ever lived". Williams has already drawn connections between this attribute and Johnson, but the spheres that GLaDOS subsequently has Chell add to Wheatley deepen this connection. Core 1's hyperactive love of space echoes Johnson's own affinity for early NASA and outrageous space exploration proposals, Core 2 (Rick the Adventure Sphere) reflects the brusque (often anti-science) American masculinity he performs, and Core 3 the inherent logical or historical contradictions which seemed to lay at the basis of his philosophy.
One could half expect, playing the final battle for the first time, Cave Johnson's personality to emerge after Chell places the last sphere. All the components were there. With the help of her mother (symbolic or otherwise), Chell had reconstructed the unreliable, absentee paternal figure of Cave Johnson. But rather than an unconventional family reunion, Wheatley is immediately ejected to the graveyard of science and engineering's heyday, a scant few feet from a lunar lander, and from there into a vacuum. Meanwhile, planetside, GLaDOS has this time intentionally thrown Chell out of her embrace, as with a child that she now recognizes is beyond her control.
Fan theories ricochet about that, like GLaDOS, the personality spheres are also based on former living beings. In that case, they are not likely to be digital reincarnations of Johnson himself, as made evident from the storyline, but the issue of heritage as it applies to the posthuman is often complex and subtle. GLaDOS, the personality cores, and indeed all of Aperture reflect in some ways the elaborate, often nonsensical minds of their foundational human influences. As I wrote in my review of Portal 2's cooperative mode:
[W]e get the impression that there is something either innate or infectious about being human, as [multiplayer robots] P-Body and Atlas develop one human-like affectation after another, much to their maker's chagrin. [We also] get the distinct impression that GLaDOS is "pining" for humanity, such that during one climactic moment it is that humanity, and nothing else, which will "save" the day. Whether GLaDOS desires human interaction because of her own suppressed human side or because she wishes to have that sort of vibrant counterpoint that she misses with Chell is left open to interpretation, but it's clear that reunification with mankind (even postapocalyptically) is of all encompassing importance by game's end.
All artificial intelligences in the Portal franchise are surprisingly anthropic from the childlike and conversational turrets to the manic, fragmentary personality cores. Only the Weighted Companion Cube, if it is indeed sentient and that isn't just a lie that GLaDOS uses to hurt Chell, is anthropomorphized in a more abstracted way, being more a reflection of player affection than the animation of emotion. All others, including P-Body and Atlas, very much go out of their way to be lively, emotional beings, proving that even a generation removed from organic life, GLaDOS's creations still exhibit their human ancestry.
As mentioned at the head of this article, there are no coincidences in games. P-Body and Atlas are designed to be relatable to the player, just as the turrets' childlike voices are meant to be unsettling. In that respect, it's easy to look at the ending of Portal 2's single-player campaign as not simply a passing of the guard from Chell onto the robots but a meeting of siblings. Moreover, it acknowledges that, Chell or robot, they are all artificial, just as their relationship to GLaDOS and ensuing events are intentionally developed conceits. It's nevertheless clear that narrative inconsistencies be damned, Chell's relationship to GLaDOS is steeped in the psychology of mother and daughter, and that by confronting and deconstructing masculine identities, she is confronting and deconstructing her father.