With the latest Klaus woobie-ism in fandom memory now, I think it’s important to point out that Caroline is not just grieving on Tyler’s behalf- she’s also grieving for Carol herself.
Just look at her face during Liz’s speech in 4x10.
They rarely have onscreen interactions (after all this is TVD, where parents drop like flies or are mostly missing), but from what we’ve been shown, I think we can assume that they were close. And it’s not just because they have similar personalities, with similar interests. Nor was it Tyler bringing them together once they started dating the summer before senior year- in fact, that drove them apart for a while.
From season 1, it would appear that Caroline spent a lot of time with Carol and that they get along famously. Their first interaction at the Founder’s Day party in 1x04 certainly makes them seem very familiar with each other: Caroline catches her eye right away at the door and Carol leaves other guests to greet her with a warm smile and they exchange kisses on the cheek. (I tried to GIF these scenes, but I just can’t seem to get a working copy of PS, so caps will have to do!)
Carol: “Caroline! You look smashing!”
Caroline: “Thank you Mrs. Lockwood. This is my boyfriend Damon.”
Carol: “Oh! Well, come on in.”
We know from 3x02 that Carol has known Caroline “since she was born,” but she treats Elena (who Tyler has “known [his] whole life” 2x14) and Bonnie very differently in the same episode- she doesn’t even acknowledge Bonnie’s presence or excuse herself as she interrupts their conversation.
Carol: “Elena honey, there you are. I’ve noticed the watch still isn’t in the collection.”
Elena: “Oh! Ah- I’m sorry Mrs. Lockwood. I couldn’t find it. I guess it’s still packed up in my parents’ stuff somewhere.”
It’s also interesting to contrast Caroline’s relationship with her own mother in 1x04: Caroline bitches at Liz for not “changing out of the badge” seconds after her warm exchange with Carol and then makes a snarky comment about her dad being with his boyfriend before stalking off
She doesn’t even look at her as they talk- it’s very much the entitled teenager judging the parent. In fact, every time Liz expresses concern about Caroline in season 1 and early season 2, she comes up with bitchy comments instead of respect.
Liz: “Honey, are you okay? Is there anything you want to talk about? (beat) Is it a boy thing?”
Caroline: “Mom. If I want to talk boys, I’ll call Dad. At least he’s successfully dating one."
Liz: “Is everything OK with you?”
Caroline: “I’m fine.
Liz: “It’s just lately you’ve seemed- different.”
Caroline: “I’m not different. I’m fine.”
Liz: “I know you don’t think I notice these things, but I do. What’s going on with you?”
Caroline: “You know- there’s pretending to be a mother and then there’s reality. Let’s not push our luck, okay?”
Carol and Caroline don’t directly interact in 1x15, but it’s telling that Caroline is in charge of selling and redeeming tickets at the bachelor raffle (a Founder’s Day fundraiser) that Carol runs. And the next time we see the two interact is at Miss Mystic in 1x19. We don’t see her response to Caroline’s enthusiastic listing of accomplishments (“I’m on the MF Beautification committee. I volunteer at the rec center soup kitchen. I implemented this year’s Go Green campaign at school, worked at the county's recycling program and was in charge of the policeman’s yearly raffle”), but we do see her giving Caroline an encouraging pat on the shoulder and smile as she is introduced, and then applauding as she makes her way down the staircase.
In contrast, we also see her nodding coolly as Elena plays her sympathy card during the interview (“This was really important to my mother.”), reprimanding Elena for “not even [being] dressed yet” and having Stefan in the dressing room, and finally brushing past Elena as she is being introduced and walking away before Elena heads down the staircase. Ouch.
The body language makes it clear who her choice was, and it seems obvious that she would choose the girl most like herself, the one who volunteers help on her events.
Season two continues to show us signs that they are close- Caroline signs up to help at Carol’s Historical society volunteer picnic in 2x05, and Carol believes her unquestioningly when Caroline tells her how Sarah died in 2x07. And after Tyler leaves Mystic Falls, Carol asks Caroline if Matt has heard from Tyler, confiding how worried she is- and Caroline reaches out and comforts her.
Finally, Caroline goes to visit Carol in the hospital after her "accident" in 2x20- not with Liz or with her friends as a buffer- just her.
Unfortunately, Carol has become suspicious of Liz’s lack of progress in ridding the town of vampires, and she gives her an ultimatum in 2x22. And then we find out in 3x01 that “when [Caroline] was over [at Tyler’s place] yesterday, [Carol] just kept eyeing [her]”. Tyler ascribes it to her “think[ing] [they’re] dating”, and we believe him- Carol also seems to have a “no girl is good enough for my son” complex judging by how she calls Vicki “trash” in 1x04 although she has voiced approval of Matt, her brother (2x06, 2x17) as Tyler’s friend. But we find out that Carol has also figured out that Caroline is a vampire when she shoots her full of vervain during her walk of shame at the end of the episode.
The next morning she likens Caroline, Miss Mystic Falls and Founding family stock, to a prostitute when she speaks to Tyler, and insists later that he “can’t be with her! She’s a monster!” She’s obviously wracked with guilt when she calls Bill to try to get him to release Caroline after Tyler’s “I’m the monster” intervention, but we are left thinking the damage to their relationship is done until 3x07, when Caroline rescues Carol from being “ghost bait.”
By 3x09 it seems that relationship is on the mend when she says to Tyler, "OK, first of all, I've finally almost just got your mother to stop hating me." But we never see them onscreen together again until 3x22, where Carol and Liz are telling Caroline and Tyler that they have to leave town together. The body language is great in this scene- both moms talk to both kids and give them both worried looks- it’s not all about their own child. As an aside, I think this makes so much sense, considering the respect with which Tyler holds Liz as well- he goes to her for help in 3x03 and the deleted scene from 3x12, and she obviously approves of him by the way she grips him on the shoulder as she’s leaving them alone in 3x03.
But the best evidence for the strength of the Carol/Caroline relationship comes from their scenes from 4x02. They don't say anything to each other in this scene, but their body language is so telling.
Neither of them look ashamed or embarrassed at all, even though it is obvious what Caroline has just been doing with Tyler. In fact, Caroline is comfortable enough with Carol to just barely cover herself with Tyler's shirt before she goes running downstairs. Neither of them care about her state of undress as they look at each other- it’s obvious that the only thing they're thinking of is Tyler, hurt and bleeding somewhere. Later in the episode Caroline’s the one assuring Carol after she unstakes Tyler- her tone is so gentle.
And from their last scene together in 4x07, it looks like that relationship is still intact despite Caroline’s fake break-up with Tyler.
They are freaking beaming at each other. And it’s fitting that the last time we see them together is at an event that they are running- they’re both control freaks who love telling people what to do and organizing events. I don’t think it’s a coincidence that their names are so similar- I think the similarity in their personalities -- both the flaws and the good points-- was a deliberate choice of the writers.
Carol is Town Mayor, and runs the Founder’s Council and Historical Society. Caroline is “student council vice-president, head of the prom committee and [she] single-handedly organized the town’s clean-up campaign” and we see her organize tonnes of events throughout the series. The parallels even show in how they talk.
Carol: “No, no, no, no, no! It’s all wrong! The marching band should be in front of the historic society. Matt, get up on the float. Boys, I asked you to put chairs on the founder’s float. Ladies! Time to get on the float!”
Caroline: “Woah, woah, woah, stop, stop! Those flowers go in the back as indicated by the floral chart that you guys had plenty of time to memorize.” “Hey, why am I bussing your tables? I said no empty glasses.” “Will you guys pick up the tempo? This is a pageant, not a funeral!”
They’re both judgemental (and tend to slut shame).
From 1x04 (referring to Vicki)
Carol: “That’s what you get when you bring the trash to the party.”
From 3x02 (referring to Caroline)
Carol: “You know, if you’re going to bring a girl home, I wish she’d have the tact not to sneak out like a prostitute.”
Caroline: “Stop hanging out with Rebekah the evil blood slut.”
Caroline: “Think of all the germ-ridden skanks that Damon has lured into his den of inequity.”
And they both notice and care about Tyler's isolation.
Carol: “It’s natural to feel abandoned. I just don’t want you to feel alone.”
Caroline: “I don’t want that to happen to you. I don’t want you to be alone.”
In fact, I think the reason that Tyler instinctively knows how to interact with Caroline in such a positive way is because of his relationship with his mother. He tells Matt how to approach Caroline before he’s even friends with her.
Matt: “She’s this amazing girl one minute and then this raging, jealous freak the next.”
Tyler: “You know what I think of Caroline Forbes? She’s an insecure neurotic bitchy little twit.”
Tyler: “But the girl’s got heart! She means well. You just got to take the good with the bad sometimes.”
That last line sums up how he interacts with both of them in a nutshell, which is why even though he usually has a low tolerance for BS –see him interact with Stefan or Matt-- he just lets the shallow, control freaky bits slide. They’re not worth calling either woman out for, because he knows that isn't the stand-out part of their personalities. The most important part of both of them is that they care. And it's really sad that both kids have lost Carol now. There really aren't enough caring parents in Mystic Falls