Mrs. Steerforth is like a walking, talking explanation for why Steerforth is such a bad person. Not that she's been abusive to him, oh no – just the opposite. She has channeled her entire emotional life into her son. So that Steerforth can continue to be comfortable in his own superiority, she deliberately sends Steerforth to a school she knows isn't going to challenge him (Salem House).
Steerforth's mother sends him to Oxford University without apparently demanding that he do any work there – as long as Steerforth keeps visiting her regularly, she gives him plenty of money and space to do whatever the hell he wants. Even Steerforth recognizes that the total lack of guidance and discipline he has received from his mother has had a bad effect on his character. But Mrs. Steerforth just keeps spoiling and indulging him.
This all comes back to bite her when David and Mr. Peggotty come to visit Mrs. Steerforth in her home at Highgate (near London). They arrive to bring her the news that Steerforth has carried away Emily. Mr. Peggotty asks if there is any chance that Steerforth will marry Emily. Mrs. Steerforth absolutely refuses: it would be bad for Steerforth's social position to marry a fisherman's daughter.
Mr. Peggotty points out that he loves his niece just as much as Mrs. Steerforth loves her son, and would do anything to help Emily. Mrs. Steerforth replies with one of the creepiest things in this book: she says that Mr. Peggotty doesn't and can't love Emily like Mrs. Steerforth loves her son.
Mrs. Steerforth's love for James Steerforth is based on her belief that he's like an extension of her. She has provided everything he could want so long as he keeps all of his emotional energies focused on her. When Steerforth takes up with Emily, Mrs. Steerforth interprets this as a rejection by her son. She thinks that Steerforth has replaced Mrs. Steerforth with Emily (*creepy*).
So, unless Steerforth gets rid of Emily, "comes humbly to [Mrs. Steerforth] and begs for [her] forgiveness" (22.119), she will never see her son again. As for Mr. Peggotty, Mrs. Steerforth shows no sympathy for his loss at all. She is totally consumed by her own feelings. And that's the main difference between the two: Mrs. Steerforth's love is utterly selfish, while Mr. Peggotty's is completely self-sacrificing.
David recognizes the same stubborn streak he has seen in Steerforth, when Mrs. Steerforth rejects her son, Mr. Peggotty, and basically the whole world, All of those glimpses David has caught of Steerforth's arrogance and unwillingness to admit he's wrong come directly from Steerforth's mother:
All that I had ever seen in him of an unyielding, willful spirit, I saw in her. All the understanding that I had now of his misdirected energy, became an understanding of her character too, and a perception that it was, in its strongest springs, the same. (22.120)
Mrs. Steerforth's character is "unyielding," and she trains her son to be equally so. Steerforth has both bad genes and a bad upbringing; perhaps if he had had a better, more careful parent, he would have survived and become a great man.
But Mrs. Steerforth gets punished by the novel for her poor training of Steerforth. When Mrs. Steerforth hears about Steerforth's sudden death, she crumples and falls as though dead. Mrs. Steerforth doesn't die, though – she lives on to old age in a state of senility, constantly yelled at and scolded by her reluctant companion, Miss Dartle. All of Mrs. Steerforth's energies were focused on her son, and once he has gone, Mrs. Steerforth has nothing left to do but live an empty, thwarted life.