Mean mommy. Cold fish. Social climber. Unfaithful wife. No, Carolyn's character is not designed to be liked… at least for the first part of American Beauty.
For the most part, the movie portrays Carolyn as a stuffy, materialistic spoiler to Lester's efforts to be happy again, so she's definitely not the most sympathetic character in the movie. American Beauty is mostly about Lester's drama and angst, so there's not as much room to delve into what might make Carolyn tick. However, we do get some glimpses into her feelings and motivations.
She's a Perfectionist
Our first glimpse of Carolyn comes when she's lovingly and painstakingly clipping the roses outside the Burnham residence so they look perfect. As Lester points out in his voiceover, her gardening clogs match the handle of her shears. She's completely concerned with perfection and appearances:
CAROLYN: Now listen to me. This is an important business function. As you know, my business is selling an image, and part of my job is to live that image…
She is very into making sure everything around her is—or at least appears to be—100% immaculate. When she and her husband almost share a moment of passion after apparently years of indifference (at best) and hostility (at worst), she interrupts it to make sure he doesn't spill beer on the couch. Lester shouts at her:
LESTER: This isn't life. This is just stuff. And it's become more important to you than living. Well, honey, that's just nuts.
But she doesn't see it that way—she is terrified of what that "stuff" might say about her, and of course that makes her look a little shallow and materialistic.
That's not to say she's totally unsympathetic, though. Early on in the film, we get to see her ritual for preparing to show a house (she's a real estate agent), and by the end of it, we do feel kind of bad for her. She carefully cleans and stages the house, repeating to herself that she's going to sell that house today, she's going to sell that house today.
Sure, it seems a little demented, but the huge importance she places on this one sale—as well as the whole "reciting mantras" thing—suggests that perhaps her self-esteem isn't super solid. Oh, and she berates herself for feeling vulnerable:
CAROLYN: Shut up. Stop it. You... Weak! You baby!
So, yeah, we do end up feeling some sympathy for her.
She's Got a Wild Side
Despite her insecurities and obsession with image, Carolyn does find time for a little fun—albeit, out of revenge. When she sees Lester cutting loose and not caring a bit about how it affects her, she decides to have some "fun" as well and sparks up an affair with her former professional rival, Buddy Kane.
She seems to enjoy it, but of course there's a vengeful quality to their "relationship"—and it takes on a violent-ish tone when Buddy gets her into shooting to help her "relax." So, unfortunately, even her attempts to have fun make her look like a maniac.
It seems like she might even be contemplating killing Lester out of anger and embarrassment at all of his shenanigans, and she arrives home the night Lester dies with a gun at the ready (and motivational tapes shouting at her not to be a "victim"). Hmm… looks like Carolyn could have been capable of some ugly stuff, if Frank Fitts hadn't beaten her to it.
As a character, Carolyn doesn't really grow or change that much, unlike pretty much all of the others. It's worth pondering why that's the case—why would Ball and Mendes choose that for her?