It was easy for Richard, living at home with a family to keep him cheerful. (2.6)
It seems that Therese resents Richard for his happy family, something she has never had.
And the husband? Therese could not see him at all. (4.30)
This is a telling statement on a few levels. One, Therese picks up that Carol is in an unhappy marriage. And two, Therese doesn't care about Carol's marriage at all—she has no qualms about pursuing Carol, even though Carol already has a family.
Then when graduation came, when she was seventeen, the school had asked her mother for two hundred dollars. Therese hadn't wanted any money from her, had half believed her mother wouldn't give her any, but she had, and Therese had taken it. (6.82)
Therese has no desire to have a relationship with her own mother. Family just isn't important to her.
"Disappeared! I like that. And how lucky you are to be able to do it. You're free. Do you realize that?" (6.97)
Carol believes that Therese is free because Therese has no family, yet Carol is tied down to a husband and a daughter.
Her mother was not dead. But Therese had not seen her since she was fourteen. (6.81)
We get a little background on Therese's family, but it never comes into play with the plot. How does it affect Therese's behavior, though? Does she see Carol as a mother figure?
"One sister. I suppose you want to know all about her, too? Her name is Elaine, she as three children and she lives in Virginia. She's older than I am, and I don't know if you'd like her. You'd think she was dull." (14.103)
Like Therese, Carol also isn't that close to her biological family—this is something Carol and Therese have in common. Carol's only family is one by marriage, and this is a bond that can (and will) be broken.
"My little orphan," Carol said. (15.52)
Is there a mother/daughter dynamic between Carol and Therese even though they are lovers? Carol says this line as if she wants to be Therese's caretaker more than her romantic partner.
"My child is my property!"
A crease twitched in his cheek. "A human being is not property, Mrs. Aird." (19.45-19.46)
The detective is a voice of reason here. Carol resents her husband because he wants to own her, but it appears that Carol feels the same way about her own daughter. She doesn't really love her; she just wants to possess her.
Yes, she understood why Carol had sent the letter. Because Carol loved her child more than her. (21.42)
We're unsure how Therese feels about this. It would be selfish if Therese resented Carol for choosing her own daughter over her, but it's understandable that Therese is hurt by her choice, too. Losing Carol would hurt regardless of the reason.
"When you have a husband and child it's a little different." (22.47)
We see Carol's family one last time as more of a burden than a source of love and affection. Her divorce and loss of custody seem more like she's freed from a ball and chain than an experience of painful loss.