Famed analytic psychologist Carl Jung once conceived of something called the mother complex or "a group of feeling-intoned ideas associated with the experience and image of mother" (source). If you took the mother complex, cranked it up to eleven, and then slapped it inside of a person, you would have Catelyn Stark.
Catelyn is a mother through and through. Her every action stems from her motherly personality, and she acts the mother to every character she meets, well with the exception of Jaime Lannister. And you really can't blame her there, seeing as the guy pushed her son Bran out a window.
Early in the novel, Catelyn has a dream where she, Ned, and their children are reunited. Arya and Sansa are holding hands, Robb is playing, and Bran can walk again (23.Catelyn.1). Of course, it's only a dream, but this dream clues us in to what motivates Catelyn: making her family whole again.
With Ned dead, Catelyn needs to save her daughters from the awful daycare that is Cersei Lannister's King's Landing, and all of her actions center on this goal. She advises Robb that if he must relinquish his crown to have Sansa and Arya returned, then he should (8.Catelyn.54). This doesn't work so well because, as she tells Brienne, "My son may be a king, but I am no queen… only a mother who would keep her children safe, however she could" (40.Catelyn.47). In the Seven Kingdoms, mothers don't get a vote—it's a "One King, One Vote" type of government.
Catelyn's attempt to barter a truce with Renly and later advise Renly and Stannis to join forces is in no way for the benefit of House Baratheon. She's looking to get Robb some allies, so he doesn't die at the hands of the Lannisters as Ned did, and when she can't perform the impossible task of bringing the Baratheon Bros together, she feels she failed her son (32.Catelyn.112).
But Catelyn's motherly tendencies extend beyond her family. Before the would-be Baratheon battle:
She knelt before the Mother, "My lady, look down on this battle with a mother's eyes. They are all sons, every one. Spare them if you can, and spare my own sons as well. Watch over Robb and Bran and Rickon. Would that I were with them." (34.Catelyn.5)
With this prayer, we see that Catelyn views the entire world through motherly eyes. She feels empathy with the knights, their suffering, and their deaths. It's not just the pain they will feel, but the sadness that will be felt by those who loved them, too—a.k.a. their mothers.
With this said, Catelyn's empathy only goes so far, and the line is drawn when it comes to her wolf cubs.
When she hears word that Bran and Rickon are "dead," she becomes understandably depressed and takes no joy in food or song or the company of others. The very woman who offered a prayer to the Mother to protect everyone instead tells Brienne, "'I want them all dead, Brienne. Theon Greyjoy first, then Jaime Lannister and Cersei and the Imp, every one, every one'" (56.Catelyn.20). The claws have officially come out, Shmoopers.
When we last see Catelyn, she's in a cell with Jaime Lannister and asking Brienne to borrow her sword. We don't find out what happens between them next, but one thing is certain: This momma wolf has had enough.